Method for producing polymer, polymer for lithography, resist composition, and method for producing substrate

ABSTRACT

A method for producing a polymer is provided. The polymer improves variations in the content ratio and molecular weights of a copolymer&#39;s constitutional units, solvent solubility, and the sensitivity of a resist composition using such a polymer. The method includes polymerizing two or more monomers while adding with a polymerization initiator to obtain the polymer, feeding a first solution containing first composition monomers in an initial polymerization stage, and starting dropwise addition of a second solution containing second composition monomers after or simultaneously with the feeding of the first solution. The second composition is equal to a target composition ratio of the polymer to be obtained. The first composition is calculated in advance based on a target composition ratio and the reactivity of the monomers. The above dropping rate is set to high.

TECHNICAL FIELD

The present invention relates to a method for producing a polymer, apolymer for lithography obtained by such a production method, acopolymer suitable for lithographic use, a resist composition containingthese polymers for lithography, and a method for producing a substratewith a pattern formed using the resist composition.

This application claims priority to Japanese Patent Application No.2009-160857 filed on Jul. 7, 2009, Japanese Patent Application No.2009-298029 filed on Dec. 28, 2009, and Japanese Patent Application No.2009-298030 filed on Dec. 28, 2009, the entire contents of which areincorporated by reference herein.

BACKGROUND ART

In recent years, in processes for manufacturing semiconductors, liquidcrystal devices, and the like, rapid progress has been made in formationof a finer pattern using lithography. Examples of technology forformation of a finer pattern include a technology using shorter waveradiation.

In recent years, KrF excimer laser (wavelength: 248 nm) lithographictechnology has been introduced. Also, ArF excimer laser (wavelength: 193nm) lithographic technology and EUV (wavelength: 13.5 nm) lithographictechnology, which are intended to use shorter wavelengths, have beeninvestigated.

Furthermore, for example, a so-called chemical amplification type resisthas been proposed as a resist compound suitably applicable to shortenthe wavelength of irradiation light and to pattern microfabrication.Such a chemical amplification type resist includes a polymer, whichbecomes soluble in alkali when an acid-eliminable group is dissociatedby the action of an acid, and a photoacid generator. The resistcomposition has been further developed and improved.

An acrylic type polymer transparent to light with a wavelength of 193 nmhas attracted attention as a chemical amplification resist polymer usedin ArF excimer laser lithography.

For example, copolymers for lithography as described in Patent Document1 below are produced using, as monomers, (A) a (meth)acrylate to whichan aliphatic hydrocarbon having a lactone ring is ester-bonded, (B) a(meth)acrylate to which a group dissociable by the action of an acid isester-bonded, and (C) a (meth)acrylate to which a hydrocarbon group oran oxygen atom-containing heterocyclic group having a polar substituentis ester-bonded.

In general, furthermore, a (meth)acrylate polymer is obtained by radicalpolymerization. Generally, in a multi-component polymer made of two ormore monomers, the monomers differ in copolymerization reaction ratio.Thus, the copolymer composition ratio of the polymers in the initialstage is different from that in the last stage. Namely, the obtainedpolymer resultantly has a composition distribution.

When a polymer has variations in the composition ratio of constitutionalunits, the solubility of the copolymer tends to be less in a solvent.Thus, the preparation of a resist composition may be affected. Forexample, preparation of a resist composition takes a long time todissolve the copolymer in a solvent, and causes an increase in thenumber of production steps due to generation of an insoluble substance.Also, the obtained resist composition tends to have insufficientsensitivity.

On the other hand, for example, a method for obtaining a polymer havinga narrow copolymer composition distribution as described in PatentDocument 2 below makes a difference between the feed rate of a monomerhaving a relatively higher polymerization rate to a monomer having alower polymerization rate in the front end of the process and that inthe back end of the process to obtain a resist having high resolution.

Also, a trace amount of a macromolecular component (high polymer)generated in the polymerization process may cause a decrease in thesolubility of a polymer for lithography in a resist solvent as well asin an alkali developing solution. As a result, the sensitivity of aresist composition is decreased.

In Patent Document 3 below, a method of limiting the generation of sucha polymer is proposed. In this method, a solution containing apolymerizable monomer and a solution containing a polymerizationinitiator are respectively held in separate reservoirs. Then, thepolymerization initiator is fed earlier than the polymerizable monomerto a polymerization system.

On the other hand, attention has been focused on an acrylic type polymertransparent to light having a wavelength of 193 nm as a chemicalamplification-type resist to be used in ArF excimer laser lithography.For example, a copolymer of a (meth)acrylate having an adamantineskeleton in the ester part and a (meth)acrylate having a lactoneskeleton in the ester part as the above acrylic type polymer (forexample, Patent Documents 4 and 5).

Incidentally, a (meth)acrylate polymer is obtained by radicalpolymerization. In a multi-component polymer produced from two or moretypes of monomers, the monomers have their respective copolymerizationreaction rates. Thus, the copolymer composition ratio of the polymer inthe initial stage is different from that in the last polymerizationstage. Namely, the resulting polymer has a composition distribution. Acopolymer having such a composition distribution tends to deteriorateresist performance. Therefore, studies have been made to control thecomposition distribution of a copolymer.

For example, from the viewpoint of solubility in solvent, PatentDocument 6 describes that the content (mol %) of a constitutional unitderived from a (meth)acrylate monomer having a lactone skeleton in eachcopolymer contained in 10 to several tens of fractions obtained bydividing a copolymer solution by gel permeation chromatography(hereinafter referred to as “GPC”) is preferably within −10 to +10 mol %of the average content of a constitutional unit derived from a(meth)acrylate monomer having a lactone skeleton in the wholecopolymers.

Also, from the viewpoint of the formation of a finer pattern insemiconductor lithography, Patent Document 7 describes that the molarcomposition of a constitutional unit having a hydroxyl group in alow-molecular-weight region corresponding to 5% of the peak of allcopolymer in GPC is preferably within ±10% of the average molarcomposition of a constitutional unit having a hydroxyl group in allcopolymer.

CITATION LIST Patent Literature

-   Patent Document 1: JP-A-2002-145955-   Patent Document 2: JP-A-2001-201856-   Patent Document 3: JP-A-2004-269855-   Patent Document 4: JP-A-H10-319595-   Patent Document 5: J JP-A-H10-274852-   Patent Document 6: PCT International Publication WO 1999/050322-   Patent Document 7: PCT International Publication WO 2005/105869

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

However, the methods described in the above Patent Documents 2 and 3 mayinsufficiently improve the solubility of a polymer for lithography orthe sensitivity of a resist composition.

The present invention has been made in consideration of the abovesituation. An object of the present invention is to provide a method forproducing a polymer, whereby the method is able to improve a variationin the content and molecular weight of a constitutional unit in acopolymer, while improving the solubility of the copolymer to a solventand the sensitivity thereof when it is used for a resist composition; apolymer for lithography obtained by the production method; a resistcomposition containing the polymer for lithography; and a method forproducing a substrate with a pattern formed thereon by using the resistcomposition.

Also, in the conventional methods as described in the above PatentDocuments 6 and 7, the solubility of a copolymer in a solvent is notsufficient. Therefore, further improvement in the solubility of acopolymer in a solvent has been desired.

In the case of, for example, a copolymer for semiconductor lithography,some disadvantages occur when preparing a composition for semiconductorlithography if the solubility of a copolymer is insufficient. Forexample, a long time is taken to dissolve the copolymer in a solvent.Also, generation of insoluble substances leads to an increase in thenumber of production steps.

Solution to the Problems

(1) In order to solve the above problem, a first aspect of the presentinvention relates to a polymerization method in which two or more typesof monomers α₁ to α_(n) (wherein n denotes an integer of 2 or more) arepolymerized while the monomers and a polymerization initiator are addeddropwise to a reactor to obtain a copolymer (P) constituted ofconstitutional units α′₁ to α′_(n) (wherein α′₁ to α′_(n) representconstitutional units derived from the monomers α₁ to α_(n)respectively), the method comprising the following two steps (I) and(II).

(I) A step of feeding a first solution containing the monomers α₁ toα_(n) in a first composition ratio in a reactor before a polymerizationinitiator is added dropwise or simultaneously with the start of thedropwise addition of the polymerization initiator, wherein proportionsof the monomers α₁ to α_(n) in the first composition ratio are thosethat enable the monomers α₁ to α_(n) to be reacted in a steady statefrom the initial stage of polymerization based on the reaction rate ofeach monomer.

(II) A step of feeding a second solution to the reactor after thefeeding of the first solution is started or simultaneously with thestart of the feeding of the first solution. When the ratio (hereinafterreferred to as “target composition ratio”) (unit:mol %) of theconstitutional units α′₁ to α′_(n) in the polymer (P) to be obtained isα′₁:α′₂: . . . :α′_(n), the second solution contains the monomers α′₁ toα′_(n) having the same composition ratio.

(2) In the polymerization method according to the first aspect, thefirst composition ratio is determined on the basis of the followingprocedures (i) to (iii).

(i) First, a dropping solution containing 100 parts by mass of a monomermixture having the same monomer composition ratio as the targetcomposition ratio, α′₁:α′₂: . . . :α′_(n), a polymerization initiatorand a solvent are added dropwise to a reactor only containing a solventat a fixed dropping rate. Then, the composition ratio (unit:mol %),M₁:M₂: . . . :M_(n), of the monomers α₁ to α_(n) left in the reactor isdetermined at each of times t₁, t₂, t₃ . . . , and t_(m) passed from thestart of the dropwise addition. In addition, a ratio (mol %) of P₁:P₂: .. . :P_(n) of the constitutional units α′₁ to α′_(n) in each of polymerswhich are produced between the time t₁ to the time t₂, between the timet₂ to the time t₃, . . . , and between the time t_(m) to the timet_(m+1) is calculated.

(ii) A time zone from t_(m) to t_(m+1) (m represents an integer of 1 ormore) when the ratio P₁:P₂: . . . :P_(n) becomes nearer to the targetcomposition ratio α′₁:α′₂: . . . :α′_(n) is determined.

(iii) Factors F₁, F₂, . . . , and F_(n) are determined from the value ofP₁:P₂: . . . :P_(n) between t_(m) and t_(m+1) and the value of M₁:M₂: .. . :M_(n) at the passage of time t_(m) according to the equationsF₁=P₁/M₁, F₂=P₂/M₂, . . . , and F_(n)=P_(n)/M_(n).

As to F₁, F₂, . . . , and F_(n), the factors calculated according to theabove procedures (i) to (iii) are represented by F₁, F₂, . . . , andF_(n), and α₁=α′₁/F₁, α₂=α′₂/F₂, . . . , α_(n)=α′_(n)/F_(n).

(3) The method for producing a polymer according to the first aspectincludes a polymerization step in which two or more types of monomers α₁to α_(n) (wherein n denotes an integer of 2 or more) are polymerizedwhile the monomers and a polymerization initiator are added dropwise toa reactor to obtain a polymer (P) constituted of constitutional unitsα′₁ to α′_(n) (wherein α′₁ to α′_(n) represent constitutional unitsderived from the monomers α₁ to α_(n) respectively).

The feeding of the first solution containing the monomers α₁ to α_(n) ina first composition ratio to the reactor is started before thepolymerization initiator is added dropwise or simultaneously with thestart of the dropwise addition of the polymerization initiator.

The dropwise addition of the second solution containing the monomers α₁to α_(n) in a second composition ratio to the reactor is started afterthe feeding of the first solution is started or simultaneously with thestart of the feeding of the first solution.

The dropwise addition of the second solution is started simultaneouslywith the start of dropwise addition of the polymerization initiator orafter the start of the dropwise addition of the polymerizationinitiator.

Here, when the ratio (unit:mol %) of the constitutional units α′₁ toα′_(n) in the polymer (P) to be obtained is the same as α′₁:α′₂: . . .:α′_(n), the second composition ratio is the same as the targetcomposition ratio.

In addition, α₁:α₂: . . . :α_(n) represents the first composition ratioand F₁, F₂, . . . , and F_(n) represent factors represented byα₁=α′₁/F₁, α₂=α′₂/F₂, . . . , and α_(n)=α′_(n)/F_(n). which arecalculated according to the following procedures (ii) to (iii).

When the passage of time since the dropwise addition of thepolymerization initiator is started until the dropwise addition of thesecond solution is stopped is defined as a standard time, the feeding ofthe first solution is completed before 20% of the standard time passes.

Furthermore, the polymerization initiator is fed in an amount of 30 to90% by mass of the total feed amount thereof during a high-rate feedingperiod.

The high-rate feeding period is a period range from 0% to j % (j is 5 to20) of the standard time, during which period the polymerizationinitiator is added dropwise at a rate higher than the average feed rate.

The average feed rate is a value obtained by dividing the total feedamount of the polymerization initiator by the standard time.

The above procedures (i) to (iii) are as follows:

(i) First, a dropping solution containing 100 parts by mass of a monomermixture having the same monomer composition ratio as the targetcomposition ratio, α′₁:α′₂: . . . :α′_(n), a polymerization initiatorand a solvent are added dropwise to a reactor only containing a solventat a fixed dropping rate; then, the composition ratio (unit:mol %),M₁:M₂: . . . :M_(n), of the monomers α₁ to α_(n) left in the reactor isdetermined at each of times t₁, t₂, t₃ . . . , and t_(m) passed from thestart of the dropwise addition. In addition, a ratio (mol %) of P₁:P₂: .. . :P_(n) of the constitutional units α′₁ to α′_(n) in each of polymerswhich are produced between the time t₁ to the time t₂, between the timet₂ to the time t₃, . . . , and between the time t_(m) to the timet_(m+1) is calculated.

(ii) A time zone from t_(m) to t_(m+1) when the ratio P₁:P₂: . . .:P_(n) becomes nearer to the target composition ratio α′₁:α′₂: . . .:α′_(n) is determined (m is an integer of 1 or more).

(iii) Factors F₁, F₂, . . . , and F_(n) are determined from the value ofP₁:P₂: . . . :P_(n) between t_(m) and t_(m+1) and the value of M₁:M₂: .. . :M_(n) at the passage of time t_(m) according to the equationsF₁=P₁/M₁, F₂=P₂/M₂, . . . , and F_(n)=P_(n)/M_(n).

(4) A second aspect of the present invention relates to a copolymer forlithography, whereby the copolymer is obtained by the above productionmethod.

Also, in view of the above problem, the inventors of the presentinvention have made earnest studies as to the solubility of a copolymer.As a result, the inventors of the present invention have found that thesolubility of a copolymer in a solvent is further improved when there isa variation in, particularly, the monomer composition of the copolymerin a high-molecular-weight region of a multi-component polymer producedfrom two or more types of monomers, to complete the present invention.

(5) Therefore, a third aspect of the present invention relates to acopolymer for lithography that is obtained by polymerizing two or moretypes of monomers. Among fractions obtained by dividing an eluateshowing peaks relative to the above copolymer in an elution curveobtained by gel permeation chromatography into eight fractions in orderof fractionation such that each fraction has the same volume, adifference between the monomer composition ratio of a copolymercontained in a first eluted fraction and the monomer composition ratioof all copolymers is −3 mol % to +3 mol % in any of the constitutionalunits derived from the respective monomers.

(6) A copolymer for lithography described in the above (4) or (5) may beused for a resist.

(7) A fourth aspect of the present invention relates a resistcomposition containing the above copolymer for lithography and acompound that generates an acid when irradiated with active rays orradial rays.

(8) A fifth aspect of the present invention relates to a method forproducing a substrate with a pattern formed thereon. The method includesthe steps of applying the above resist composition to the surface of asubstrate to form a resist film, exposing the resist film to light, anddeveloping the exposed resist film by using a developing solution.

Effects of the Invention

According to the above production method, a copolymer can be obtainedwhich can improve a variation in the ratio of a constitutional unit anda variation in molecular weight of the constitutional unit and can alsoimprove the solubility thereof in a solvent and the sensitivity thereofwhen used as a resist composition.

A variation in the ratio of a constitutional unit of the copolymer forlithography and a variation in molecular weight of the constitutionalunit are improved. Also, the copolymer for lithography has goodsolubility in a solvent. Also, high sensitivity is obtained byformulating the copolymer for lithography in a resist composition.

Also, the above copolymer for lithography is reduced in a variation inthe monomer composition of the copolymer in a high-molecular-weightregion. Also, the copolymer for lithography has good solubility in asolvent. Also, high sensitivity is obtained by formulating the copolymerfor lithography in a resist composition.

The above resist composition is a chemical amplification type. Also, thesolubility of the copolymer in a resist solvent is good. Thus, thecontent of insoluble materials in the composition is small. Also, theabove resist composition has excellent sensitivity.

According to the above method for producing a substrate, a highlyprecise and fine resist pattern reduced in defects can be formed stably.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph representing the results of Reference Example 1.

FIG. 2 is a graph representing the results of Reference Example 1.

FIG. 3 is a graph representing the results of Example 1.

FIG. 4 is a graph representing the results of Example 1.

FIG. 5 is a graph representing the results of Example 2.

FIG. 6 is a graph representing the results of Example 2.

FIG. 7 is a graph representing the results of Reference Example 2.

FIG. 8 is a graph representing the results of Reference Example 2.

FIG. 9 is a graph representing the results of Example 3.

FIG. 10 is a graph representing the results of Example 3.

FIG. 11 is a graph representing the results of Reference Example 1.

FIG. 12 is a graph representing the results of Example 1.

FIG. 13 is a graph representing the results of Example 2.

FIG. 14 is a graph representing the results of Reference Example 2.

FIG. 15 is a graph representing the results of Reference Example 3.

FIG. 16 is a view typically representing an example of an elution curve.

DESCRIPTION OF EMBODIMENTS

In this specification, the term “(meth)acrylic acid” means acrylic acidor methacrylic acid. The term “(meth)acryloyloxy” means acryloyloxy ormethacryloyloxy.

In this specification, the weight-average molecular weight (Mw) andmolecular weight distribution (Mw/Mn) of polymer are those in terms ofpolystyrene measured by gel permeation chromatography.

In this specification, the copolymer means a copolymer obtained bypolymerizing two or more types of monomers α₁ to α_(n) (wherein ndenotes an integer of 2 or more) and constructed of constitutional unitsα′₁ to α′_(n) (wherein α′_(i) represents a constitutional unit derivedfrom the monomer α_(i), i denotes an integer from 2 to n, and n denotesan integer of 2 or more). The monomer composition ratio of the copolymermeans the ratio (unit:mol %) of each constitutional unit based on allconstitutional units of the copolymer.

In this specification, the copolymer for lithography is, for example, acopolymer for resist and a copolymer for an antireflection film. Thecopolymer for lithography is suitable to use for lithography.

(Production Method)

<Polymer (P)>

The polymer (P) in the present invention is composed of constitutionalunits α′₁ to α′_(n) (wherein α′₁ to α′_(n) represent constitutionalunits derived from the monomers α₁ to α_(n) and n denotes an integer of2 or more). Here, n is preferably 6 or less from the point that theadvantageous effects of the present invention can be easily obtained. Inaddition, n is more preferably 5 or less and even more preferably 4 orless when the polymer (P) is a resist polymer.

When, for example, n=3, the polymer (P) is a ternary polymer P(α′₁/α′₂/α′₃) constituted of constitutional units α′₁, α′₂ and α′₃. Whenn=4, the polymer (P) is a quaternary polymer P (α′₁/α′₂/α′₃/α′₄)constituted of constitutional units α′₁, α′₂, α′₃ and α′₄.

There is no particular limitation to the use of the above polymer (P).For example, the above polymer (P) is preferably a polymer forlithography that is used in a lithographic step. Examples of the polymerfor lithography include a resist polymer, polymer for an antireflectionfilm that is used for forming an antireflection film (TARC) formed onthe topside of a resist film or antireflection film (BARC) formed on thebackside of a resist film, polymer for a gap-fill film used for forminga gap-fill film, and polymer for a topcoat film used for forming atopcoat film.

The weight-average molecular weight (Mw) of the polymer for lithographyis preferably 1,000 to 200,000, and more preferably 2,000 to 40,000. Thedistribution of molecular weight (Mw/Mn) is preferably 1.0 to 10.0 andmore preferably 1.1 to 4.0.

There is no particular limitation to the constitutional unit of thepolymer (P) and the constitutional unit is suitably selected accordingto use and requirements.

When the above polymer is a resist copolymer, the above polymerpreferably has a constitutional unit having an acid-dissociable group.When the above polymer is a resist polymer, the above polymer may haveknown constitutional units such as a constitutional unit having alactone skeleton and a constitutional unit having a hydrophilic groupaccording to the need. The weight-average molecular weight (Mw) of thepolymer (P) for a resist is preferably 1,000 to 100,000 and morepreferably 3,000 to 30,000. The distribution of molecular weight (Mw/Mn)is preferably 1.0 to 3.0 and more preferably 1.1 to 2.5.

The polymer for an antireflection film preferably has a constitutionalunit having, for example, a light-absorbing group. This polymerpreferably has a constitutional unit having a functional group that iscurable by reaction with a curing agent and the like to avoid mixing ofthe resist film with the polymer for an antireflection film. Examples ofthis reactive functional group include an amino group, an amide group, ahydroxyl group, and an epoxy group.

The light-absorbing group is a group having high ability to absorb lightthat can sensitize light-sensitive components in the resist compositionand has a wavelength falling in a prescribed wavelength range. Specificexamples of the light-absorbing group include a group having a ringstructure (may have optional substituents) such as an anthracene ring, anaphthalene ring, a benzene ring, a quinoline ring, a quinoxaline ring,and a thiazole ring. When KrF laser light is used as the radiationlight, the light-absorbing group is preferably an anthracene ring oranthracene rings having optional substituents. When ArF laser light isused as the radiation light, the light-absorbing group is preferably abenzene ring or benzene rings having optional substituents.

Examples of the above optional substituent include a phenolic hydroxylgroup, alcoholic hydroxyl group, carboxyl group, carbonyl group, estergroup, amino group, or amide group.

Particularly, a polymer for an antireflection film which contains aprotective or non-protective phenolic hydroxyl group as this substituentis preferable from the viewpoint of obtaining good developingcharacteristics and high resolution.

Examples of the constitutional unit/monomer having the abovelight-absorbing group include benzyl(meth)acrylate andp-hydroxyphenyl(meth)acrylate.

The polymer for a gap-fill film preferably has a suitable viscosityallowing it to flow into a narrow gap. Moreover, the polymer for agap-fill film preferably has a constitutional unit having a reactivefunctional group that is curable by reacting with a curing agent toavoid the mixing of the gap-fill film polymer with the resist film orantireflection film.

Specific examples of the polymer for a gap-fill film include copolymersof hydroxystyrene and monomers such as styrene, alkyl(meth)acrylate andhydroxyalkyl(meth)acrylate.

Examples of the polymer for a topcoat film that is used for immersionlithography include copolymers containing a constitutional unit having acarboxyl group and copolymers containing a constitutional unit having afluorine-containing group substituted with a hydroxyl group.

<Constitutional Unit/Monomer>

The polymer (P) is obtained by polymerizing monomers α₁ to α_(n)corresponding to constitutional units α′₁ to α′_(n). The monomer ispreferably a compound having a vinyl group. The monomer is preferably acompound that is radically polymerized with ease. Particularly,(meth)acrylate has high transparency to exposure light having awavelength of 250 nm or less.

Hereinafter, constitutional units and monomers corresponding to theconstitutional units when the polymer (P) is a resist polymer aredescribed.

(Constitutional Unit/Monomer Having an Acid-Eliminable Group)

The resist polymer preferably has an acid-eliminable group. The term“acid-eliminable group” used herein is a group having a bond cleaved bythe action of an acid. Some or all of the acid-eliminable groups areeliminated from the main chain of the polymer by the above cleavage ofthe bond.

In the composition for a resist, the polymer having a constitutionalunit having an acid-eliminable group reacts with an acid component to besoluble in an alkaline solution, thereby contributing the formation of aresist pattern.

The proportion of the constitutional unit having an acid-eliminablegroup based on all constitutional unit (100 mol %) constituting thepolymer is preferably 20 mol % or more and more preferably 25 mol % ormore from the viewpoint of sensitivity and resolution. This proportionis preferably 60 mol % or less, more preferably 55 mol % or less, andeven more preferably 50 mol % or less from the viewpoint of adhesion toa substrate or the like.

Any monomer may be used as the monomer having an acid-eliminable groupas long as it has an acid-eliminable group and a polymerizable multiplebond. A known compound may be used as the monomer having anacid-eliminable group. The polymerizable multiple bond means a multiplebond which is cleaved in a polymerization reaction to form a copolymerchain. The polymerizable multiple bond is preferably an ethylenic doublebond.

Specific examples of the monomer having an acid eliminable group include(meth)acrylates having an aliphatic hydrocarbon group having 6 to 20carbon atoms and an acid-dissociable group. The above aliphatichydrocarbon group may be connected to an oxygen atom constituting theester bond of the (meth)acrylate either directly or through a connectinggroup such as an alkylene group.

The above (meth)acrylate has, for example, an aliphatic hydrocarbongroup having 6 to 20 carbon atoms. Also, the (meth)acrylate is, forexample, a (meth)acrylate having a tertiary carbon atom at the positionwhere it is bonded with an oxygen atom constituting an ester bond, or a(meth)acrylate containing an aliphatic hydrocarbon group having 6 to 20carbon atoms which is bonded to a —COOR group (R represents a tertiaryhydrocarbon group, a tetrahydrofuranyl group, a tetrahydropyranyl group,or an oxepanyl group, which may have a substituent) directly or througha connecting group.

When, particularly, a resist composition to be applied to a patternformation method using light having a wavelength of 250 nm or less toexpose is produced, preferable examples of the monomer containing anacid-eliminable group include 2-methyl-2-adamantyl(meth)acrylate,2-ethyl-2-adamantyl(meth)acrylate,1-(1′-adamantyl)-1-methylethyl(meth)acrylate,1-methylcyclohexyl(meth)acrylate, 1-ethylcyclohexyl(meth)acrylate,1-methylcyclopentyl(meth)acrylate, 2-ethylcyclopentyl(meth)acrylate,2-isopropyl-2-adamantyl(meth)acrylate, and1-ethylcyclooctyl(meth)acrylate.

Among these compounds, 1-ethylcyclohexylmethacrylate (m-2 in Examples),2-methyl-2-adamantylmethacrylate (m-5 in Examples),1-ethylcyclopentylmethacrylate and 2-isopropyl-2-adamantylmethacrylateare more preferable. The constitutional unit having an acid-eliminablegroup may be used singly or in combination of two or more, as necessary.

(Constitutional Unit/Monomer Having Polar Group)

The term “polar group” is a group having a polar functional group or apolar atomic group. Specific examples of the “polar group” include ahydroxy group, a cyano group, an alkoxy group, a carboxyl group, anamino group, a carbonyl group, a fluorine atom-containing group, asulfur atom-containing group, a lactone skeleton-containing group, anacetal structure-containing group, and an ether bond-containing group.

Among these groups, the resist polymer to be applied to a patternformation method using light having a wavelength of 250 nm or less toexpose preferably has a constitutional unit having a lactone skeleton.Moreover, the resist polymer preferably has a constitutional unit havinga hydrophilic group that will be described later.

(Constitutional Unit/Monomer Having Lactone Skeleton)

Examples of the lactone skeleton include lactone skeletons having abouta 4- to 20-membered ring. The lactone skeleton may be a single ring onlycontaining a lactone ring or may contain a lactone ring and an aliphaticor aromatic carbon ring or hetero-ring condensed with the lactone ring.

When the copolymer contains a constitutional unit having a lactoneskeleton, the content of the constitutional unit is preferably 20 mol %and more preferably 35 mol % or more based on all constitutional units(100 mol %) from the viewpoint of adhesion to, for example, thesubstrate. Also, the content is preferably 60 mol % or less, morepreferably 55 mol % or less and even more preferably 50 mol % or lessfrom the viewpoint of sensitivity and resolution.

The monomer having a lactone skeleton is preferably at least one typeselected from the group consisting of methacrylates having a substitutedor unsubstituted δ-valerolactone and monomers having a substituted orunsubstituted γ-butyrolactone ring, and more preferably a monomer havingan unsubstituted γ-butyrolactone ring.

Specific examples of the monomer having a lactone skeleton includeβ-(meth)acryloyloxy-β-methyl-δ-valerolactone,4,4-dimethyl-2-methylene-γ-butyrolactone,β-(meth)acryloyloxy-γ-butyrolactone,β-(meth)acryloyloxy-β-methyl-γ-butyrolactone,α-(meth)acryloyloxy-γ-butyrolactone,2-(1-(meth)acryloyloxy)ethyl-4-butanolide, pantoyllactone(meth)acrylate, 5-(meth)acryloyloxy-2,6-norbornanecarbolactone,8-methacryloxy-4-oxatricyclo[5.2.1.0^(2,6)]decan-3-one, and9-methacryloxy-4-oxatricyclo[5.2.1.0^(2,6)]decan-3-one. Also, examplesof a monomer having an analogous structure includemethacryloyloxysuccinic acid anhydride.

Among these compounds, α-methacryloyloxy-γ-butyrolactone (m-1 inExamples), α-acryloyloxy-γ-butyrolactone (m-4 in Examples),5-metacryloyloxy-2,6-norbornanecarbolactone, and8-methacryloxy-4-oxatricylo[5.2.1.0^(2,6)]decan-3-one are morepreferable.

One type of monomer having a lactone skeleton may be singly used. Two ormore types of monomers having a lactone skeleton may be combined uponuse.

(Constitutional Unit/Monomer Having Hydrophilic Group)

The term “hydrophilic group” in this specification means at least onetype among —C(CF₃)₂—OH, hydroxy group, cyano group, methoxy group,carboxyl group, and amino group.

Among these groups, the resist polymer which is applied to the patternformation method using light having a wavelength of 250 nm or less toexpose preferably has a hydroxy group or cyano group as the hydrophilicgroup.

The content of the constitutional unit having a hydrophilic group in thecopolymer based on all constitutional units (100 mol %) is preferably 5to 30 mol % and more preferably 10 to 25 mol % from the viewpoint of therectangularity of a resist pattern.

Examples of the monomer having a hydrophilic group include:(meth)acrylates having a terminal hydroxy group; derivatives having asubstituent, such as an alkyl group, a hydroxy group, or a carboxylgroup, on a hydrophilic group of a monomer; and monomers having a cyclichydrocarbon group (for example, cyclohexyl(meth)acrylate,1-isobornyl(meth)acrylate, tricylodecanyl(meth)acrylate,dicyclopentyl(meth)acrylate, 2-methyl-2-adamantyl(meth)acrylate, and2-ethyl-2-adamantyl(meth)acrylate) and having a hydrophilc group, suchas a hydroxy group or a carboxyl group, as a substituent.

Specific examples of the monomer having a hydrophilic group include a(meth)acrylic acid, 2-hydroxyethyl(meth)acrylate,3-hydroxypropyl(meth)acrylate, 2-hydroxy-n-propyl(meth)acrylate,4-hydroxybutyl(meth)acrylate, 3-hydroxyadamantyl(meth)acrylate, 2- or3-cyano-5-norbornyl(meth)acrylate, and2-cyanomethyl-2-adamantyl(meth)acrylate. Among them,3-hydroxyadamantyl(meth)acrylate, 2- or3-cyano-5-norbornyl(meth)acrylate, and2-cyanomethyl-2-adamantyl(meth)acrylate are preferable from theviewpoint of adhesion to the substrate.

Among these compounds, 3-hydroxyadamantyl(meth)acrylate (m-3 inExamples) and 2-cyanomethyl-2-adamantyl(meth)acrylate (m-6 in Example)are more preferable.

These monomers having a hydrophilic group may be used either singly orin combinations of two or more.

(Constitutional Unit Having Structure that Absorbs Radial Rays)

When the copolymer of the present invention is a polymer for anantireflection film, it is necessary that the copolymer contain amolecular structure that absorbs radial rays applied in a lithographicstep.

The structure that absorbs radial rays differs depending on thewavelength of the radial rays to be used. The structure absorbing radialrays is preferably a naphthalene skeleton and anthracene skeleton to KrFexcimer laser light. The structure absorbing radial rays is preferably abenzene skeleton to ArF excimer laser light.

Examples of the monomer providing constitutional units having thesemolecular structures may include styrenes such as styrene,α-methylstyrene, p-methylstyrene, p-hydroxystyrene, and m-hydroxystyreneand their derivatives, and aromatic group-containing esters having anethylenic double bond such as substituted or unsubstitutedphenyl(meth)acrylates, substituted or unsubstitutednaphthalene(meth)acrylates, and substituted or unsubstitutedanthracenemethyl(meth)acrylate.

The proportion of the constitutional unit having a molecular structureabsorbing radial rays based on all constitutional units (100 mol %) ofthe copolymer is preferably 10 to 100 mol %.

<Polymerization Initiator>

Polymerization initiators, which are decomposed by heat to generateradicals efficiently, are preferable. It is also preferable to use apolymerization initiator having a ten-hour half-life temperature lowerthan the polymerization temperature. When, for example, a polymer forlithography is produced, the polymerization temperature is preferably 50to 150° C. Also, when a polymer for lithography is produced, it ispreferable to use a polymerization initiator having a ten-hour half-lifetemperature of 50 to 70° C.°. In order that the polymerization initiatorbe decomposed efficiently, the difference between the ten-hour half-lifetemperature and polymerization temperature of the polymerizationinitiator is preferably 10° C. or more.

Examples of the polymerization initiator include azo compounds such as2,2′-azobisisobutyronitrile, dimethyl-2,2′-azobisisobutylate,2,2′-azobis(2,4-dimethylvaleronitrile), and2,2′-azobis[2-(2-imidazoline-2-yl)propane and organic peroxides such as2,5-dimethyl-2,5-bis(tert-butylperoxy)hexane, anddi(4-tert-butylcyclohexyl)peroxydicarbonate. Azo compounds are morepreferable.

These compounds are available as commercial products. For example,dimethyl-2,2′-azobisisobutylate (trade name: V601, manufactured by WakoPure Chemical Industries Ltd., ten-hour half-life temperature: 66° C.)and 2,2′-azobis(2,4-dimethylvaleronitrile (trade name: V65, manufacturedby Wako Pure Chemical Industries Ltd., ten-hour half-life temperature:51° C.) may be preferably used.

<Solvent>

A polymerization solvent may be used in the method for producing apolymer according to the present invention. For example, any one of thefollowing polymerization solvents may be used.

Ethers: chain ether (for example, diethyl ether and propylene glycolmonomethyl ether), cyclic ethers (for example, tetrahydrofuran(hereinafter referred to as “THF” where necessary), 1,4-dioxane and thelike.

Esters: methyl acetate, ethyl acetate, butyl acetate, ethyl lactate,butyl lactate, propylene glycol monomethyl ether acetate (hereinafterreferred to as “PGMEA” where necessary), γ-butyrolactone and the like.

Ketones: acetone, methyl ethyl ketone, methyl isobutyl ketone and thelike.

Amides: N,N-dimethylacetamide, N,N-dimethylformamide and the like.

Sulfoxides: dimethylsulfoxide and the like.

Aromatic hydrocarbons: Benzene, toluene, xylene and the like.

Aliphatic hydrocarbons: hexane and the like.

Alicyclic hydrocarbons: cyclohexane and the like.

One type of polymerization solvent may be singly used. Also, two or moretypes of polymerization solvents may be combined prior to use.

The amount of the polymerization solvent is, for example, preferablysuch an amount that the solid content of a solution (polymerizationreaction solution) in a reactor is about 20 to 40% by mass when thepolymerization reaction is completed, though no particular limitation isimposed on the amount.

<Method for Producing a Polymer>

A method for producing a polymer comprises a polymerization step inwhich two or more types of monomers α₁ to α_(n) are polymerized whilethe monomers and a polymerization initiator are added dropwise to areactor to obtain a polymer (P) constituted of constitutional units α′₁to α′_(n) (wherein α′₁ to α′_(n) represent constitutional units derivedfrom the monomers α₁ to α_(n) respectively). The polymerization step isperformed by the radical polymerization method. In the presentinvention, the dropping polymerization method is used in which themonomers are polymerized while the monomers and a polymerizationinitiator are added dropwise to a reactor.

In the present invention, a first solution containing the monomers α₁ toα_(n) in a first composition ratio and a second solution containing themonomers α₁ to α_(n) in a second composition ratio are used as solutionscontaining monomers. The first and second solutions each preferably havea solvent.

(Second Solution)

The ratio of the contents (second composition ratio) of the monomers inthe second solution is equal to the target composition ratio showing theratio of the contents of the constitutional units α′1 to α′n in thepolymer (P) to be obtained.

For example, when the polymer (P) is a ternary polymer obtained bycopolymerizing monomers x, y and z and the target composition ratio (mol%, the same as follows) is x′:y′:z′, the second composition ratio (mol%, the same as follows) x:y:z is equal to x′:y′:z′.

The second solution is dripped to feed it in the reactor.

(First Solution)

The ratio of the contents (first composition ratio) of the monomers inthe first solution is determined in advance from the target compositionratio of the polymer (P) taking the reactivity of each monomer used inthe polymerization into account.

To describe in more detail, when the ratio of the contents of themonomers existing in the reactor is the first composition ratio, thefirst composition ratio is designed so that the ratio of the contents ofthe constitutional units of a polymer molecule generated just after theabove second solution is added dropwise to the reactor is equal to thetarget composition ratio. In this case, the ratio of the contents of theconstitutional units of a polymer molecule generated just after theabove second solution is added dropwise is equal to the ratio of thecontents (target composition ratio) of the monomers in the secondsolution to be added dropwise, and therefore, the content ratio of themonomers left in the reactor just after the dropwise addition is alwaysfixed (first composition ratio). Therefore, when the second solution issuccessively added dropwise to such a reactor, a stationary state underwhich a polymer molecule having the target composition ratio issuccessively produced is obtained.

There has been no information regarding a first composition enablingsuch a stationary state prior to the present invention. This is afinding first obtained by the inventors of the present invention. Amethod of designing the first composition will be described later.

The reactor may be charged with the first composition in advance. Also,the first solution may be gradually fed to the reactor by adding itdropwise or the like. Alternatively, these feed methods may be combined.

(Polymerization Initiator)

The polymerization initiator is added dropwise and fed to the reactor.The second solution may contain the polymerization initiator. For addingthe first solution dropwise to the reactor, the first solution maycontain the polymerization initiator. A solution containing thepolymerization initiator may be added dropwise to the reactor separatelyfrom the first and second solutions. Alternatively, these solutions maybe combined together.

The amount of the polymerization initiator to be used (the whole amountof the polymerization initiator to be fed) is designed on the basis ofthe type of polymerization initiator or according to the target value ofthe weight-average molecular weight of the polymer (P).

For example, when the polymer (P) in the present invention is a polymerfor lithography, the amount of the polymerization initiator (the totalamount thereof to be fed) based on 100 mol % of the sum (whole feedamount) of the monomers fed to the reactor is preferably in a range from1 to 25 mol % and more preferably in a range from 1.5 to 20 mol %.

(Content of Monomers)

The total amount of monomers to be used in polymerization (whole amountof the monomers to be fed) is the sum of the total amount of themonomers contained in the first solution and the total amount of themonomers contained in the second solution. The whole amount of themonomers to be fed is designed on the basis of the amount of the polymer(P) to be obtained.

When the ratio of the total amount of the monomers contained in thefirst solution in the whole amount of the monomers is too small, theintended effect obtained by the use of the first solution isinsufficiently obtained. When the proportion is too large on the otherhand, the molecular weight of the polymer produced in the early stage ofthe polymerization process becomes too large. Therefore, the totalamount of the monomers contained in the first solution based on thetotal amount of the monomer to be fed is preferably 3 to 40% by mass andmore preferably 5 to 30% by mass.

(Polymerization Step)

In the polymerization step, it is necessary that the first solutionexist in the reactor when the polymerization initiator is added dropwiseto the reactor. Therefore, the feeding of the first solution to thereactor is started before the polymerization initiator is added dropwiseto the reactor or simultaneously with the start of the dropwise additionof the polymerization initiator.

It is also necessary that the first solution exist in the reactor whenthe second solution is added dropwise to the reactor. Therefore, thefeeding of the second solution to the reactor is started after thefeeding of the first solution to the reactor is started orsimultaneously with the start of the feeding of the first solution. Thedropwise addition of the second solution is started simultaneously withthe start of the dropwise addition of the polymerization initiator orafter the start of the dropwise addition of the polymerizationinitiator. The dropwise addition of the polymerization initiator and thedropwise addition of the second solution are preferably started at thesame time.

The second solution may be added dropwise either continuously orintermittently and the second solution may be added dropwise at a variedrate. The second solution may be preferably added dropwise continuouslyat a constant rate to stabilize the composition and molecular weight ofthe polymer to be produced.

When the first solution is fed by dropwise addition, it may be addeddropwise either continuously or intermittently. Also, the first solutionmay be added dropwise at a varied rate. The first solution may bepreferably added dropwise continuously at a constant rate to stabilizethe composition and molecular weight of the polymer to be produced.

The whole amount of the first solution is preferably fed in the initialstage of the polymerization step. To describe in more detail, when thestandard time is a time elapsed since the dropwise addition of thepolymerization initiator is started until the dropwise addition of thesecond solution is completed, the feeding of the first solution isstopped before 20% of the above standard time is elapsed. When thestandard time is, for example, 4 hours, the whole amount of the firstsolution is fed to the reactor before 48 minutes elapses after the startof the dropwise addition of the polymerization initiator.

The feeding of the first solution is completed before preferably 15% andmore preferably 30% of the standard time elapses.

Also, the feeding of the whole amount of the first solution may becompleted at 0% of the standard time. In other words, the reactor may becharged with the whole amount of the first solution before the start ofthe dropwise addition of the polymerization initiator.

The feed amount of the polymerization initiator in the initial stage ofthe polymerization step is increased. To describe in detail, when anaverage feed rate Vj is a value obtained by dividing the whole feedamount of the polymerization initiator by the standard time, a periodfrom 0% to j % (j is 5 to 20) of the standard time is defined as thehigh-rate feeding period of the polymerization initiator. During thehigh-rate feeding period, the polymerization initiator is added dropwiseat a rate higher than the average feed rate Vj.

The high-rate feeding period of the polymerization initiator begins atthe start of the standard time, that is, 0% of the standard time. Thehigh-rate feeding period of the polymerization initiator terminates whenj % of the standard time elapses. The above j % is in a range from 5 to20%, preferably 5.5 to 17.5% and more preferably 6 to 15%.

The amount of the polymerization initiator to be fed to the reactor inthe high-rate feeding period is 30 to 90% by mass of the whole feedamount of the polymerization initiator. The weight-average molecularweight of the polymer generated in the early stage of the polymerizationstep varies corresponding to the amount of the polymerization initiatorto be fed during the high-rate feeding period. Therefore, the optimumamount of the polymerization initiator to be fed during the high-ratefeeding period differs depending on the types of monomers, feed rate ofthe monomers, type of polymerization initiator and polymerizationcondition. However, the optimum amount of the polymerization initiatoris preferably set so that the weight-average molecular weight of thepolymer generated particularly in the early stage of the polymerizationstep is close to the target value. The above feed amount is preferably35 to 85% by mass and more preferably 40 to 80% by mass of the wholefeed amount of the polymerization initiator.

It is necessary that the rate of dropwise addition of the polymerizationinitiator during the high-rate feeding period be kept higher than theabove average feed rate. The rate of dropwise addition of thepolymerization initiator may be changed during the course of thehigh-rate feeding period.

It is necessary that the rate of dropwise addition of the polymerizationinitiator after the end of the high-rate feeding period be lower thanthe above average feed rate. The rate of dropwise addition of thepolymerization initiator may be changed during the course of the processafter the end of the high-rate feeding period. The polymerizationinitiator may be added dropwise either continuously or intermittently.

The dropwise addition of the polymerization initiator is preferablycompleted after the feeding of the first solution is completed orsimultaneously with completion of the feeding of the first solution.

Although the dropwise addition of the polymerization initiator and thedropwise addition of the second solution are preferably completedsimultaneously, the finish times of both may be slightly different fromeach other to the extent that the effect of the present invention is notimpaired.

Preferable examples of the embodiment of the polymerization step includethe following (a) and (b).

(a) The reactor is charged with the first solution containing themonomers α₁ to α_(n) in the first composition in advance. Then, thesolution in the reactor is heated to a predetermined polymerizationtemperature, and then, a polymerization initiator solution containing apart of the polymerization initiator and the second solution containingthe monomers α₁ to α_(n) in the second composition and the rest of thepolymerization initiator are respectively added in the above reactor.The dropwise addition of the polymerization initiator solution and thedropwise addition of the second solution are started simultaneously orthe dropwise addition of the polymerization initiator solution isstarted first. The dropwise addition of the polymerization initiatorsolution and the dropwise addition of the second solution are preferablystarted simultaneously. The time elapsing since the start of thedropwise addition of the polymerization initiator solution until thestart of the dropwise addition of the second solution is preferably 0 to10 minutes.

The rates of dropwise addition are each preferably fixed. The dropwiseaddition of the polymerization initiator solution is completed beforethe dropwise addition of the second solution.

In this embodiment, when the dropwise addition of the polymerizationinitiator solution is started, the standard time starts, that is, thedropwise addition of the polymerization is started. In this embodiment,before the dropwise addition of the polymerization initiator is started,the whole amount of the first solution is fed to the reactor.Specifically, the feeding of the first solution is completed at 0% ofthe standard time. The high-rate feeding period is a period during whichthe polymerization initiator solution is added dropwise. The amount ofthe polymerization initiator to be fed to the reactor during thehigh-rate feeding period is the sum of the amount of the polymerizationinitiator contained in the polymerization initiator solution and amountof the polymerization initiator contained in the second solution addeddropwise for the period during which the polymerization initiatorsolution is added dropwise. The dropwise addition of the polymerizationinitiator is completed when the dropwise addition of the second solutionis completed.

(b) The reactor is charged only with a solvent. Then, the solvent isheated to a predetermined polymerization temperature, and then, thefirst solution containing the monomers α₁ to α_(n) in the firstcomposition ratio and a part of the polymerization initiator and thesecond solution containing the monomers α₁ to α_(n) in the secondcomposition ratio and the rest of the polymerization initiator and therest of the polymerization initiator are respectively added in the abovereactor. The dropwise additions of both solutions are startedsimultaneously or the dropwise addition of the first solution is firststarted. The time elapsing since the start of the dropwise addition ofthe first solution until the start of the dropwise addition of thesecond solution is preferably 0 to 10 minutes.

The rates of dropwise additions of the first solution and secondsolution are each preferably fixed. The dropwise addition of the firstsolution is completed before the dropwise addition of the secondsolution.

In this embodiment, the dropwise addition of the polymerizationinitiator is started simultaneously with the start of the dropwiseaddition of the first solution. The high-rate feeding period is a periodduring which the first solution is added dropwise. The amount of thepolymerization initiator to be fed to the reactor during the high-ratefeeding period is the sum of the amount of the polymerization initiatorcontained in the first solution and amount of the polymerizationinitiator contained in the second solution added dropwise for the periodduring which the first solution is added dropwise. The dropwise additionof the polymerization initiator is completed when the dropwise additionof the second solution is completed.

According to the method of the present invention, the first and secondsolutions in which the content ratio of the monomers is designed so thatthe aforementioned stationary state is obtained are used, ensuring thata polymer molecule having the same composition ratio as the targetcomposition ratio is produced just after the start of a polymerizationreaction.

Therefore, a variation in the percentage of the constitutional unit inthe polymer (P) obtained after the polymerization step is reduced. Thisleads to an improvement in the solubility of the polymer in the solventand in the sensitivity of a resist composition containing the polymer.

According to the method of the present invention, in addition, the firstsolution containing the monomers is fed before the early stage of thepolymerization step and also, the early stage of the polymerization stepis designed to be the high-rate feeding period of the polymerizationinitiator, ensuring that a variation in weight-average molecular weightas a function of reaction time is reduced. This improves the solubilityof the polymer in a solvent and the sensitivity of a resist compositioncontaining the polymer. This may be due to the fact that the generationof a polymer molecule having an excessively high weight-averagemolecular weight is limited.

Therefore, according to the present invention, the polymer (P) that hasgood solubility in a solvent and can constitute a highly sensitiveresist composition can be obtained with high reproducibility.

It is to be noted that the polymer of the present invention may beapplied to use in applications other than resist applications. Inaddition, according to the polymer of the present invention, asolubility-improving effect can be obtained. Furthermore, improvementsin various performances can be expected.

<Method of Designing First Composition Ratio>

A method of designing the first composition ratio will be described.

When α′₁:α′₂: . . . :α′_(n) is the content ratio (target compositionratio, unit:mol %) of the constitutional units in the polymer (P) to beobtained, α₁:α₂: . . . :α_(n) represents the first composition (unit:mol%), and F₁, F₂, . . . and F_(n), are factors calculated according to thefollowing procedures (i) to (iii).

(i) First, a dropping solution containing 100 parts by mass of a monomermixture having the same monomer composition as the target compositionratio, α′₁:α′₂: . . . :α′_(n), a polymerization initiator and a solventare added dropwise to a reactor only containing a solvent at a fixeddropping rate. Then, the composition ratio (unit:mol %), M₁:M₂: . . .:M_(n), of the monomers α₁ to α_(n) left in the reactor is determined ateach of times t₁, t₂, t₃ . . . , and t_(m) passed from the start of thedropwise addition. In addition, a ratio (mol %) of P₁:P₂: . . . :P_(n)of the constitutional units α′₁ to α′_(n) in each of polymers which areproduced between the time t₁ to the time t₂, between the time t₂ to thetime t₃, . . . , and between the time t_(m) to the time t_(m+1) iscalculated.

(ii) A time zone from t_(m) to t_(m+1) (m represents an integer of 1 ormore) when the ratio P₁:P₂: . . . :P_(n) becomes nearest to the targetcomposition ratio α′₁:α′₂: . . . :α′_(n) is determined.

(iii) Factors F₁, F₂, . . . , and F_(n) are determined from the value ofP₁:P₂: . . . :P_(n) between t_(m) and t_(m+1) and the value of M₁:M₂: .. . :M_(n) at the passage of time t_(m) according to the equationsF₁=P₁/M₁, F₂=P₂/M₂, . . . , and F_(n)=P_(n)/M_(n).

When, for example, the polymer (P) is a ternary polymer obtained bycopolymerizing monomers x, y and z, and the target composition ratio isx′:y′:z′, to explain in more detail, the first composition ratio (mol %,the same as follows) x₀:y₀:z₀ are defined as values obtained by thefollowing equations x₀=x′/Fx, y₀=y′/Fy and z₀=z′/Fz by using the factorsFx, Fy and Fz calculated by the following method.

(Method of Calculating the Factors Fx, Fy and Fz)

The case where the polymer (P) is, for example, a ternary polymer willbe described. However, the factors can be calculated in the same mannereven in the case where the polymer (P) is a binary polymer or aquaternary or more multiple component polymer.

(1) First, dropping solution containing a monomer mixture having thesame monomer composition ratio as the target composition ratio x′:y′:z′,a solvent and a polymerization initiator is added dropwise at a constantdropping rate v in a reactor. The reactor is charged only with a solventprior to the addition.

The composition ratio (unit:mol %), Mx:My:Mz, of the monomers x, y and zleft in the reactor at each of times t₁, t₂, t₃ . . . , and t_(m) fromthe start of the dropwise addition is determined. In addition, a ratio(mol %) of Px:Py:Pz of the constitutional units in each of polymersproduced between the time t₁ to the time t₂, between the time t₂ to thetime t₃, . . . , and between the time t_(m) to the time t_(m+1) iscalculated.

(2) A time zone from t_(m) to t_(m+1) (m represents an integer of 1 ormore) when the ratio Px:Py:Pz becomes nearest to the target compositionratio x′:y′:z′ is determined.

(3) Factors Fx, Fy, and Fz are determined from the value of Px:Py:Pzbetween t_(m) and t_(m+1) and the value of Mx:My:Mz at the passage oftime t_(m) according to the equations Fx=Px/Mx, Fy=Py/My, Fz=Pz/Mz.

The factors Fx, Fy and Fz are respectively a value reflecting therelative reactivity of each monomer. Also, when the combination of themonomers or target composition ratio used in the polymerization ischanged, the factors Fx, Fy and Fz are changed.

(4) Preferably, the proportion (W₀% by mass) of the total mass of themonomers existing in the reactor at the above passage of time tm isdetermined based on 100% by mass of the monomer mixture contained in thefirst dropping solution.

In the method of the present invention, the effect of producing apolymer molecule having the same composition as the target compositionratio is easily obtained just after the start of the polymerizationreaction, when the proportion of the total amount of the monomerscontained in the first solution based on the whole feed amount of themonomers is W₀% by mass.

<Resist Composition>

The resist composition of the present invention is prepared bydissolving the polymer for lithography of the present invention in aresist solvent. The resist solvent is, for example, the same one as theabove polymerization solvent used in the production of the polymer.

When the resist composition of the present invention is a chemicalamplification-type resist composition, it further contains a compound(hereinafter referred to as a photoacid generator) that generates anacid by irradiation with active rays or radial rays.

(Photoacid Generator)

As the photoacid generator, an appropriate one may be selected fromknown photoacid generators in chemical amplification type resistcompositions. One type of photoacid generator may be used singly. Also,two or more photoacid generators may be used in combination.

Examples of the photoacid generator include onium salt compounds,sulfoneimide compounds, sulfone compounds, sulfonate compounds,quinonediazide compounds, and diazomethane compounds.

The content of the photoacid generator in the resist composition ispreferably 0.1 to 20 parts by mass and more preferably 0.5 to 10 partsby mass based on 100 parts by mass of the polymer.

(Nitrogen-Containing Compound)

The chemical amplification type resist composition may contain anitrogen-containing compound. When the chemical amplification typeresist composition contains a nitrogen-containing compound, furtherimprovements in the shape of a resist pattern and post exposurestability can be attained. Namely, the sectional shape of a resistpattern becomes closer to a rectangular shape. Also, in amass-production line of a semiconductor, there is the case where aresist film is allowed to stand for several hours after the resist filmis irradiated with light and then baked (PEB). However, in thisembodiment, deterioration in the sectional shape of a resist patterncaused by such a condition that the resist pattern is allowed to stand(deterioration with time) is more restrained.

The nitrogen-containing compound is preferably an amine, more preferablya secondary lower aliphatic amine, and a tertiary lower aliphatic amine.

The content of the nitrogen-containing compound in the resistcomposition is preferably 0.01 to 2 parts by mass based on 100 parts bymass of the polymer.

(Organic Carboxylic Acid and Oxoacid of Phosphorous or its Derivatives)

The chemical amplification type resist composition may contain anorganic carboxylic acid and oxoacid of phosphorous or its derivatives(hereinafter these compounds are collectively called acid compounds).When the chemical amplification type resist composition contains an acidcompound, deterioration in sensitivity caused by the formulation of anitrogen-containing compound can be restrained. Also, furtherimprovements in the shape of a resist pattern and post exposurestability can be attained.

Examples of the organic carboxylic acid include malonic acid, citricacid, malic acid, succinic acid, benzoic acid and salicylic acid.

Examples of oxoacid of phosphorous or its derivatives include phosphoricacid or its derivatives, phosphonic acid or its derivatives andphosphinic acid or its derivatives.

The content of the acid compound in the resist composition is preferably0.01 to 5 parts by mass.

(Additives)

The resist composition of the present invention may contain a surfactantand other additives such as a quencher, a sensitizer, ahalation-preventive agent, a storage stabilizing agent, and anantifoaming agent if needed. All additives known in the above field maybe used as the additives. Also, no particular limitation is imposed onthe amount of these additives, and the amount of these additives may beoptionally determined.

<Method for Producing Substrate with Pattern Formed Thereon>

An example of a method for producing a substrate with a pattern formedthereon according to the present invention will be described.

First, the resist composition of the present invention is applied by thespin coating method to the surface of a substrate such as a siliconwafer on which a desired fine pattern is to be formed. Then, thesubstrate coated with the resist composition is dried by a bakingtreatment (prebaked) to thereby form a resist film on the substrate.

Then, the resist film is exposed to light through a photomask to form alatent image. The exposure light is preferably light having a wavelengthof 250 nm or less. The exposure light is preferably a KrF excimer laser,ArF excimer laser, F2 excimer laser and EUV light and more preferably anArF excimer laser. Immersion exposure may be performed in which theresist film is irradiated with light in the condition that a liquidhaving a high refractive index is interposed between the resist film andthe final lens of the exposure apparatus. The liquid having a highrefractive index is, for example, pure water,perfluoro-2-butyltetrahydrofuran, and perfluorotrialkylamine.

After being exposed to light, the resist film is heat-treated (bakedafter being exposed, PEB). Then, an alkali developing solution isbrought into contact with the resist film. Then, the exposed part isdissolved in the developing solution. Then, the developing solution isremoved (developing). Examples of the alkali developing solution includeknown alkali developing solutions.

After the developing, the substrate is suitably rinse-treated. A resistpattern is formed on the substrate by this treatment.

The resist of the substrate on which the resist pattern is formed isreinforced by suitable heat treatment (post-baking). Then, the part onwhich no resist is formed is selectively etched.

After the etching, the resist is removed by a releasing agent to obtainthe substrate on which a fine pattern is formed.

The polymer for lithography obtained by the production method of thepresent invention has excellent solubility in a solvent and enables theformation of a resist film having high sensitivity.

Therefore, when the resist composition is prepared, the polymer can bedissolved easily and well in a resist solvent. Also, the resistcomposition has excellent solubility in an alkali developing solution.This contributes to an improvement in sensitivity. Also, becauseinsoluble substances in the resist composition are small, defects causedby the insoluble substances are scarcely generated.

According to the method for producing a substrate according to thepresent invention, therefore, a highly precise and fine resist patternreduced in defects can be formed stably by using the resist compositionof the present invention. Also, the resist composition of the presentinvention may be preferably used even in the case of forming a patternby photolithography using exposure light having a wavelength of 250 nmor less or electron beam lithography, for example, lithography using anArF excimer laser (193 nm) though it is required to use a resistcomposition having high sensitivity and high resolution in these kindsof lithography.

It is to be noted that when a resist composition is used inphotolithography using exposure light having a wavelength of 250 nm orless, monomers suitably selected so that the polymer is transparent toexposure light having the above wavelength are preferably used.

<Division of a Copolymer by GPC>

Furthermore, in the case of the copolymer of the present invention, aneluate shows peaks relevant to the copolymer in an elution curveobtained by GPC. The eluate is divided into eight equal-volume fractionsin order of fractionation. A difference between the monomer compositionratio of a copolymer contained in a first eluted fraction and themonomer composition ratio of all copolymers is −3 mol % to +3 mol % inany of the constitutional units derived from each monomer.

FIG. 16 schematically illustrates an example of an elution curve in GPC.The abscissa is an elution volume V (elution rate×elution time). Theelution volume V is a cumulative volume of an eluate that flows out ofthe column and passes through the detector. The ordinate is a signalintensity detected when the eluate passes through the detector.Generally, when the distribution of molecular weight of the polymer ismeasured using GPC, the logarithm of the molecular weight of the polymerin the eluate passing through the detector monotonously decreases withincrease in elution volume V. Specifically, a molecule having a largermolecule elutes earlier from the column. Also, the signal intensity isproportional to the existence amount of the polymer in the eluatepassing through the detector.

The eluate exhibiting a peak originated from the copolymer in an elutioncurve obtained by GPC means the eluate passing through the detectorbetween the peak start (represented by the sign S in FIG. 16) and peakend (represented by the sign E in FIG. 16) of the signal intensity inthe elution curve.

In this case, a base line B is drawn on the elution curve. S is a pointof intersection between the elution curve on the small elution volumeside and the base line B. Also, E is a point of intersection between theelution curve on the large elution volume side and the base line B.

Also, the description “an eluate showing peaks is divided into eightfractions in order of fractionation such that each fraction has the samevolume” means that the elution volume V between the peak start S and thepeak end E is divided into eight equal parts in order of elution asshown by the dotted line in FIG. 16 and then, the eluate correspondingto each elution volume after being divided is separated as a fraction.Specifically, the elution volume V is divided into eight fractions tocollect the eluate as illustrated in FIG. 16. These eight fractions arerespectively called: fraction F1 obtained between the elution volumes V1and V2; fraction F2 obtained between the elution volumes V2 and V3;fraction F3 obtained between the elution volumes V3 and V4; fraction F4obtained between the elution volumes V4 and V5; fraction F5 obtainedbetween the elution volumes V5 and V6; fraction F6 obtained between theelution volumes V6 and V7; fraction F7 obtained between the elutionvolumes V7 and V8; and fraction F8 obtained between the elution volumesV8 and V9.

In the present invention, the monomer composition ratio (hereinafterreferred to as a divisional monomer composition ratio where necessary)of the copolymer contained in a first-eluted fraction among the obtainedeight fractions is measured. The first-eluted fraction means a fractionwhen the elution volume V is smallest. This is, for example, thefraction F1 obtained between the elution volumes V1 and V2. A polymerhaving a higher molecular weight is contained in a smaller elutionvolume. There is the case where a first-eluted fraction is referred toas “high-molecular-weight fraction” where necessary in thisspecification.

The monomer composition ratio of the copolymer contained in the fractioncan be determined by analyzing a GPC-fractionated solution (i.e.,fraction) by ¹H-NMR.

<Measurement of Monomer Composition Ratio of all Copolymers>

In the present invention, the monomer composition ratio (hereinafteralso referred to as “average monomer composition ratio) of allcopolymers before divided by GPC is also measured.

The average monomer composition ratio in the present invention may beanalyzed using an infrared spectroscopy (IR) or nuclear magneticresonance spectroscopy (NMR). A more precise value can be obtained bycalculating the average monomer composition ratio from a ratio of aspecific 1H signal intensities obtained by measuring the copolymer by¹H-NMR.

In the copolymer of the present invention, a difference between thedivisional monomer composition ratio and the average copolymercomposition ratio is −3 mol % to +3 mol % and preferably −2.6 mol % to+2.6 mol % in any of the constitutional units derived from each monomer.

When, for example, the copolymer is a ternary polymer constituted ofconstitutional units α′₁, α′₂ and α′₃ and the composition ratios (alsocalled content ratios, unit:mol %) of the constitutional units α′₁, α′₂and α′₃ in the average monomer composition ratio are X mol %, Y mol %and Z mol %, the content ratio (unit:mol %) of the constitutional unitα′₁ in the divisional monomer composition ratio is in a range from (X−3)mol % to (X+3) mol % and preferably in a range from (X−2.6) mol % to(X+2.6) mol %.

Also, the content ratio (unit:mol %) of the constitutional unit α′₂ inthe divisional monomer composition ratio is in a range from (Y−3) mol %to (Y+3) mol % and preferably in a range from (Y−2.6) mol % to (Y+2.6)mol %.

Similarly, the content ratio (unit:mol %) of the constitutional unit α′₃in the divisional monomer composition ratio is in a range from (Z−3) mol% to (Z+3) mol % and preferably in a range from (Z−2.6) mol % to (Z+2.6)mol %.

If a difference between the divisional monomer composition ratio in theaforementioned high-molecular-weight fraction and the whole averagemonomer composition ratio is within ±3 mol %, the solubility of thecopolymer in a solvent is efficiently improved as shown by the examplesdescribed later. Also, the sensitivity of a resist compositioncontaining the above copolymer is improved.

The reason of obtaining such a solubility-improving effect is asfollows.

Generally, the amount of each monomer to be used in the synthesis of acopolymer is determined on the basis of the target value of an intendedmonomer composition ratio. Also, a polymerization condition and the likeare so designed that the average monomer composition ratio in asynthesized copolymer becomes close to the above target monomercomposition ratio.

However, because the copolymerization reactivity rates of monomers to becopolymerized differ from each other in many cases, the monomers are notcopolymerized at random. This causes a deviation from the target monomercomposition ratio. Also, according to the finding of the inventors ofthe present invention, the monomer composition ratio of a producedcopolymer also differs corresponding to a difference in reaction time(polymerization rate). Particularly, the monomer composition ratios ofcopolymers produced in the early and last stages tend to differ largelyfrom the target value.

On the other hand, a solvent to be used in a composition for lithographyis selected in accordance with the target value of the monomercomposition ratio. It is therefore inferred that a deviation from thetarget monomer composition ratio impairs the solubility in a solvent.

In particular, a higher-molecular-weight compound may be generally lesssoluble in a solvent and therefore, a variation in monomer compositionratio in a high-molecular-weight region further impairs the solubility.

The molecular weight of the copolymer contained in thehigh-molecular-weight fraction in the present invention corresponds to ahigh-molecular-weight region in a range of the upper rank 12.5%(one-eighth) in the distribution of molecular weight of all copolymers.In the copolymer of the present invention, a deviation from the averagemonomer composition ratio is small in such a high-molecular-weightregion. Therefore, good solubility of the copolymer may be obtainedbecause of a small deviation from the target monomer composition ratio.

Also, a deviation in monomer composition ratio in all copolymers may bealso reduced because of a small variation in monomer composition ratioin the high-molecular-weight region. Therefore, high sensitivity may beobtained by formulating the copolymer in a resist composition.

EXAMPLES

The present invention will be described in more detail by way ofexamples, which are however not intended to limit the present invention.In these examples, reference examples and comparative example, alldesignations of parts indicate parts by weight, unless otherwise noted.

Examples 1 to 3, Reference Examples 1 and 2, and Comparative Examples 1and 2

The following measuring methods and evaluation methods were used.

(Measurement of Weight Average Molecular Weight)

The weight-average molecular weight (Mw) and distribution of molecularweight (Mw/Mn) of the polymer were determined in terms of polystyrene bygel permeation chromatography under the following conditions (GPCconditions).

(GPC Conditions)

Apparatus: trade name: Tosoh High-speed GPC apparatus HLC-8220GPC,manufactured by Tosoh Co., Ltd.;

Separation column: column prepared by connecting three columns (tradename: Shodex GPC K-805 L) in series;

Measuring temperature: 40° C.;

Eluent: tetrahydrofuran (THF);

Sample (in the case of a polymer): solution obtained by dissolving about20 mg of a polymer in 5 mL of THF and by filtering the solution by a0.5-μm membrane filter;

Sample (in the case of a polymerization reaction solution): solutionobtained by dissolving about 30 mg of a polymerization reaction solutionin 5 mL of THF and by filtering the solution by a 0.5-μm membranefilter;

Flow rate: 1 mL/min;

Charge amount: 0.1 mL; and

Detector: differential reflectometer

Calibration curve I: about 20 g of standard polystyrene was dissolved in5 mL of THF. Then, the mixture solution was filtered through a 0.5-μmmembrane filter to obtain a solution, which was then poured into aseparation column in the above condition. Then, the relationship betweenelution time and molecular weight was determined. The following standardpolyethylene (all products are represented by trade names) was used asthe standard polyethylene.

F-80 (Mw=706,000);

F-20 (Mw=190,000);

F-4 (Mw=37,900);

F-1 (Mw=10,200);

A-2500 (Mw=2,630); and

A-500 (mixture of polystyrenes having Mw=682, 578, 474, 370, and 260).

(Quantitative Measurement of Monomer)

The amount of a monomer left in a polymerization reaction solution wasdetermined by the following methods.

First, 0.5 g of the polymerization reaction solution in the reactor wassampled. Then, the sample solution was diluted to a total volume of 50ml with acetonitrile using a measuring flask. This diluted solution wasfiltered through a 0.2-μm membrane filter. Then, the amount of anunreacted monomer in the above diluted solution was determined for everytype of monomer by using a high-performance liquid chromatograph (tradename: HPLC-8020, manufactured by Tosoh Co., Ltd.).

The measurement was made under the following conditions. Specifically,one separation column (trade name: Inertsil ODS-2, manufactured by GLSciences Inc.) was used as the separation column. A water/acetonitrilegradient type was used as the mobile phase. The flow rate was designedto be 0.8 mL/min. As the detector, an ultraviolet-visible absorptiometer(trade name: UV-8020, manufactured by Tosoh Co., Ltd.) was used. Thedetection wavelength was designed to be 220 nm. The measuringtemperature was designed to be 40° C. The pouring amount was designed tobe 4 μL. Also, Inertsil ODS-2 (trade name, particle diameter of silicagel: 5 μm and column inside diameter 4.6 mm×column length 450 mm) wasused as the separation column. Also, the gradient condition of themobile phase was designed to be as follows. The solution A is water. Thesolution B is acetonitrile. In order to quantitatively measure theamount of an unreacted monomer, three types of each monomer solutiondiffering in concentration were used as standard solutions.

Measuring time 0 to 3 min: solution A/solution B=90 vol %/10 vol %.

Measuring time 3 to 24 min: solution A/solution B=90 vol %/10 vol % to50 vol %/50 vol %.

Measuring time 24 to 36.5 min: solution A/solution B=50 vol %/50 vol %to 0 vol %/100 vol %.

Measuring time 36.5 to 44 min: solution A/solution B=0 vol %/100 vol %.

(Evaluation of Solubility of Polymer)

20 parts of the polymer and 80 parts of PGMEA were mixed. Then, themixture was stirred at 25° C. while measuring the time required fordissolving the polymer completely. It was determined whether the polymerwas completely dissolved or not.

(Evaluation of Sensitivity of Resist Composition)

The resist composition was applied to a 6-inch silicon wafer withrotation. Then, the wafer was prebaked (PAB) at 120° C. on a hot platefor 60 seconds to form a resist film 300 nm in thickness. Using an ArFexcimer laser exposure apparatus (trade name: VUVES-4500, manufacturedby Litho Tech Japan Corporation), 18 shots having an area of 10 mm×10 mmwere exposed to light at varied doses. Then, the resist film waspost-baked (PEB) at 110° C. for 60 seconds. After that, using a resistdeveloping analyzer (trade name: RDA-806, manufactured by Litho TechJapan Corporation), the resist film was developed at 23.5° C. by anaqueous 2.38% tetramethylammonium solution for 65 seconds. The resistfilm exposed at each dose was measured to detect a variation in resistfilm thickness with time during developing.

The relationship between the logarithm of the exposure dose(unit:mJ/cm²) and the proportion (unit:%, hereinafter referred to as aresidual film ratio) of a residual film thickness with respect to theinitial film thickness when the resist film was developed for 30 secondswas plotted based on the obtained data of the variation in filmthickness with time, to make a dose-residual film ratio curve. Based onthis curve, the value of the exposure dose (Eth) required to reduce theresidual film ratio to 0% was determined. Specifically, the exposuredose (mJ/cm²) at the point where the dose-residual film ratio curvecrosses a line of 0% residual film ratio was determined as Eth. This Ethvalue indicates the sensitivity of the resist composition. As this valuebecomes smaller, the sensitivity of the resist composition becomeshigher.

Reference Example 1 Design of First Composition Ratio

In this example, a first composition ratio was determined in the case ofpolymerizing monomers m-1, m-2 and m-3 represented by the followingformulae (m-1), (m-2) and (m-3) respectively to produce a polymer sodesigned that its target composition ratio was m-1:m-2:m-3=40:40:20 (mol%) and its target value of molecular weight was 10,000.

The polymerization initiator used in the present invention wasdimethyl-2,2′-azobisisobutylate (trade name: V601, mentioned above). Thepolymerization temperature was set to 80° C.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, a dropping funnel, and a temperature gauge was charged with67.8 parts of ethyl lactate in a nitrogen atmosphere. The flask wasbathed. Then, the bath temperature was raised to 80° C. while stirringthe content in the flask.

Then, a dropping solution (total amount: 205.725 g) containing thefollowing monomer mixture, solvent and polymerization initiator wasprepared. Then, this solution was added dropwise over 4 hours to theflask at a fixed dropping rate by using the dropping funnel. Then, theflask was kept at 80° C. for 3 hours. After 7 hours passed since thedropwise addition of the dropping solution was started, the flask wascooled to ambient temperature to stop the reaction.

Monomer m-1: 28.56 parts (40 mol %);

Monomer m-2: 32.93 parts (40 mol %);

Monomer m-3: 19.82 parts (20 mol %);

Ethyl lactate: 122.0 parts; and

Dimethyl-2,2′-azobisisobutylate:2,415 parts (2.5 mol % of the total feedamount of the monomers).

When 0.5, 1, 2, 3, 4, 5, 6 and 7 hours passed after the drop-wiseaddition of the above dropping solution was started, 0.5 g of thepolymerization reaction solution was sampled at each time. Then, theamounts of the monomers m-1 to m-3 were respectively measuredquantitatively. From this, the mass of each monomer left in the reactoris determined. As a result, for example, the results obtained 2 hoursand 3 hours after the dropwise addition is started are shown in Table 1.

TABLE 1 After 2 hrs (parts by mass) After 3 hrs (parts by mass) Monomerm-1 4.00 4.00 Monomer m-2 7.24 7.75 Monomer m-3 2.89 2.90

Then, the mass of each monomer was converted into the mol ratio(corresponding to Mx:My:Mz) of each monomer left in the reactor at eachtime of sampling by using the molecular weight of each monomer. As aresult, for example, the results obtained 2 hours and 3 hours after thedropwise addition was started are shown in Table 2.

TABLE 2 After 2 hrs (mol %) After 3 hrs (mol %) Monomer m-1 (Mx) 32.3531.20 Monomer m-2 (My) 50.79 52.49 Monomer m-3 (Mz) 16.86 16.31

On the other hand, the total mass of each monomer fed until eachsampling time was determined from the mass (total feed amount) of eachmonomer fed to the reactor at a fixed rate for 4 hours. Then, withregard to each monomer, the mass of the monomer left in the reactor ateach sampling time was subtracted from this total mass to therebycalculate the mass of the monomer converted into a polymer at eachsampling time among the monomer fed until the sampling time.

Then, with regard to each monomer, data of a difference between eachsampling time was taken to find the mass of the monomer converted into apolymer between each sampling time. Then, this mass was converted into amolar fraction. The value of this molar fraction corresponds to thecontent ratio (hereinafter also referred to as a polymer compositionratio) Px:Py:Pz of the constitutional units in a polymer producedbetween each sampling time. The term “a polymer produced between eachsampling time” means each polymer produced while the times (reactiontimes) elapsed from the start of dropwise addition were from t₁ to t₂,from t₂ to t₃, and from t_(m) to t_(m+1).

The obtained results are shown in FIG. 1 and FIG. 11. The abscissa inFIG. 1 is the end side reaction time of each reaction time zone (betweeneach sampling time). In FIG. 1, when, for example, the reaction time ofthe abscissa is 3 hours, the data corresponds to the data of a polymerproduced between 2 hours and 3 hours after the start of the dropwiseaddition (same as follows). The reaction time of the abscissa in FIG. 1is replaced with each cumulative polymerization (reaction) rate (%) toobtain a graph of FIG. 11.

Also, the weight-average molecular weight (Mw) and distribution ofmolecular weight (Mw/Mn) of the polymerization reaction solutionobtained by sampling at each reaction time were determined by GPCmeasurement. The results are shown in Table 3 and FIG. 2.

The reaction time in Table 3 and FIG. 2 is the end side reaction time ofeach reaction time zone (between sampling times). When, for example, thereaction time of the abscissa is 3 hours, the data corresponds to thedata of a polymer produced between 2 hours and 3 hours after the startof the dropwise addition (same as follows).

TABLE 3 Reaction time (hrs) Mw Mw/Mn 0.5 9400 1.75 1 11900 1.98 2 120001.71 3 10900 2.04 4 10800 1.80 5 10300 1.91 6 10200 2.07 7 9900 2.16

As shown by the results in FIG. 1, the polymer composition ratio(Px:Py:Pz) in a polymer produced 2 hours to 3 hours after the dropwiseaddition was started was closest to the target composition ratio40:40:20. The value of the polymer composition ratio was as follows:Px:Py:Pz=41.05:38.47:20.48.

Using this value and the value (Table 2) Mx:My:Mz obtained 2 hours afterthe dropwise addition was started, the factors Fx, Fy and Fz werecalculated according to Fx=Px/Mx, Fy=Py/My and Fz=Fz/Mz, to find thatFx=1.27, Fy=0.76, and Fz=1.22.

The above factor and target composition ratio were used to find a firstcomposition ratio x₀:y₀:z₀.

x₀=40/Fx=40/1.27=31.3 mol %

y₀=40/Fy=40/0.76=52.4 mol %

z0=20/Fz=20/1.22=16.3 mol %

(Calculation of W₀)

The ratio (W₀) occupied by the total mass (14.13 parts from Table 1) ofthe monomer existing in the reactor 2 hours after the start of thedropwise addition in a monomer mixture (total of 81.31 parts) containedin the first dropping solution is 17.4% by mass.

Example 1

In this example, a polymer was produced using the first compositionratio determined in Reference Example 1 by the above method (a)according to the present invention. The type of monomer, type ofpolymerization initiator, polymerization temperature, target compositionratio of the polymer and target value of the weight-average molecularweight in use are the same as those in Reference Example 1.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, two dropping funnels and a temperature gauge was charged withthe following first solution in a nitrogen atmosphere. The flask wasbathed. Then, the bath temperature was raised to 80° C. while stirringthe content in the flask.

Then, the following second solution was added dropwise to the flask byusing the dropping funnel over 4 hours. Then, the flask was kept at 80°C. for 3 hours. Also, the following polymerization initiator solutionwas added dropwise to the flask by using another dropping funnel for0.25 hours simultaneously with the start of the dropwise addition of thesecond solution. The flask was cooled to ambient temperature toterminate the reaction 7 hours after the dropwise addition of the secondsolution was started.

The ratio occupied by the monomer contained in the first solution basedon the total feed amount of the monomers was set to 17.4% by massaccording to W₀ in Reference Example 1.

In this example, the standard time is 4 hours. Also, the high-ratefeeding period is the period (0.25 hours) during which thepolymerization initiator solution was added dropwise. Specifically, thehigh-rate feeding period (0 to j %) is 0 to 6.25% (j=6.25%) of thestandard time. The polymerization initiator to be fed to the reactorduring high-rate feeding period is about 65% by mass of the total feedamount of the polymerization initiator.

(First Solution)

Monomer m-1: 3.87 parts (31.3 mol %);

Monomer m-2: 7.46 parts (52.4 mol %);

Monomer m-3: 2.80 parts (16.3 mol %); and

Ethyl lactate: 96.5 parts.

(Second Solution)

Monomer m-1: 23.34 parts (40 mol %);

Monomer m-2: 26.91 parts (40 mol %);

Monomer m-3: 16.20 parts (20 mol %);

Ethyl lactate: 98.9 parts; and

Dimethyl-2,2′-azobisisobutylate: 0.670 parts (0.7 mol % based on thetotal feed amount of the monomers).

(Polymerization Initiator Solution)

Ethyl lactate: 1.9 parts; and

Dimethyl-2,2′-azobisisobutylate: 1.243 parts (1.3 mol % based on thetotal feed amount of the monomers)

The content ratio (polymer composition ratio) of the constitutionalunits of a polymer produced in each reaction time was determined. Theresults are shown in FIG. 3. The reaction time of the abscissa in FIG. 1is replaced with each cumulative polymerization (reaction) rate (%) toobtain a graph of FIG. 12.

Also, the weight-average molecular weight (Mw) and distribution ofmolecular weight (Mw/Mn) of the polymerization reaction solutionobtained by sampling at each reaction time were determined in the samemanner as in Reference Example 1. The results are shown in Table 4 andFIG. 4.

TABLE 4 Reaction time (hrs) Mw Mw/Mn 0.5 9400 1.99 1 9000 1.89 2 92001.84 3 9600 1.81 4 9800 1.83 5 9700 1.83 6 9500 1.85 7 9500 1.83

The results shown in FIG. 1 and FIG. 3 are compared. In ReferenceExample 1 (FIG. 1), the polymer composition ratio of a polymer producedjust after the dropwise addition was started largely deviates from thetarget composition ratio. Also, there is a large variation in polymercomposition according to the reaction time.

In Example 1 (FIG. 3) in which the flask was charged with the firstsolution in advance, the polymer composition ratio was, on the otherhand, almost equal to the target composition ratio at any time justafter the dropwise addition was started. A variation in compositionratio corresponding to the reaction time was also improved.Particularly, the polymer composition ratio of a polymer obtained untilthe reaction time is 4 hours by continuous dropwise addition differs alittle from the target composition ratio.

The results of FIG. 11 and FIG. 12 are compared with each other. InReference Example 1 (FIG. 11), the polymer composition ratio of apolymer produced just after the start of the dropwise addition largelydeviates from the target composition ratio from the viewpoint ofcumulative polymerization (reaction) rate (%). Also, there is a largevariation in polymer composition.

In Example 1 (FIG. 12) in which the flask is charged with the firstsolution in advance, the polymer composition ratio is almost equal tothe target composition ratio at any time just after the start of thedropwise addition. Particularly, the polymer composition ratio of apolymer obtained until the cumulative polymerization (reaction) ratereaches 80% or more by continuous dropwise addition differs a littlefrom the target composition ratio.

Also, the results of FIG. 2 and FIG. 4 are compared. In Reference 1(FIG. 2), particularly, the weight-average molecular weight obtained 3hours after the start of the dropwise addition largely differs from thatof a polymer obtained after that time. Also, there is a large variationcorresponding to the reaction time.

In Example 1 (FIG. 4), on the other hand, there are small variations inweight-average molecular weight and distribution of molecular weightcorresponding to the reaction time just after the start of the dropwiseaddition until the end of the reaction.

(Refining of Polymer)

After the reaction was continued for 7 hours, the flask was cooled toambient temperature to terminate the reaction. Then, the polymerizationreaction solution in the flask was added dropwise to a mixture solventof methanol and water (methanol/water=80/20 ratio by volume) having avolume ten times that of the reaction solution while stirring to obtaina white precipitate (polymer P1). The precipitate was separated byfiltration. Then, the separated precipitate was again poured into amixture solvent of methanol and water (methanol/water=90/10 ratio byvolume) having the same amount as above. Then, the mixture was washedwhile stirring. Then, the washed precipitate was separated by filtrationto obtain 160 g of a wet polymer powder. Subsequently, 10 g of the wetpolymer powder was dried at 40° C. under reduced pressure for about 40hours. Mw and Mw/Mn of the obtained polymer P1 were determined. Also,the solubility of the polymer P1 was evaluated. The results are shown inTable 10.

(Production of Resist Composition)

The rest of the above wet polymer powder was poured into 880 g of PGMEA.Then, the above wet polymer powder was completely dissolved to obtain apolymer solution. This polymer solution was passed through a nylonfilter (trade name: P-NYLON N66FILTER 0.04 M, manufactured by Nihon PallLtd.) having a pore size of 0.04 μm to filter the polymer solution.

The obtained polymer solution was heated under reduced pressure todistill methanol and water. Further, PGMEA was distilled from thepolymer solution. A polymer P1 solution was thus obtained. Theconcentration of the polymer in the polymer P1 solution was 25% by mass.In this case, the maximum ultimate vacuum was 0.7 kPa. The maximumsolution temperature was 65° C. Also, the time required for distillationwas 8 hours.

400 parts of the obtained polymer P1 solution, 2 parts oftriphenylsulfonium triflate provided as a photoacid generator and PGMEAprovided as a solvent were mixed such that the concentration of thepolymer was 12.5% by mass to obtain a homogeneous solution. Thissolution was then subjected to filtration using a membrane filter havinga pore size of 0.1 μm to obtain a resist composition. The sensitivity ofthe resist composition was evaluated by the above method. The resultsare shown in Table 10.

Example 2

In this example, a polymer was produced using the first compositionratio determined in Reference Example 1 by the above method (b)according to the present invention. The type of monomer, type ofpolymerization initiator, polymerization temperature, target compositionratio of the polymer and target value of the weight-average molecularweight in use are the same as those in Reference Example 1.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, two dropping funnels and a temperature gauge was charged with86.5 parts of ethyl acetate in a nitrogen atmosphere. The flask wasbathed. Then, the bath temperature was raised to 80° C. while stirringthe content in the flask.

Then, the following second solution was added dropwise to the flask byusing the dropping funnel over 4 hours. Then, the flask was kept at 80°C. for 3 hours. Also, the following first solution was added dropwise tothe flask over 0.25 hours by using another dropping funnelsimultaneously with the start of the dropwise addition of the secondsolution. The flask was cooled to ambient temperature to terminate thereaction 7 hours after the dropwise addition of the second solution wasstarted.

The ratio occupied by the monomer contained in the first solution basedon the total feed amount of the monomers was set to 17.4% by massaccording to W₀ in Reference Example 1.

In this example, the standard time is 4 hours. Also, the high-ratefeeding period is the period (0.25 hours) during which the firstsolution was added dropwise. Specifically, the high-rate feeding period(0 to j %) is 0 to 6.25% (j=6.25%) of the standard time. Thepolymerization initiator to be fed to the reactor during high-ratefeeding period is about 65% by mass of the total feed amount of thepolymerization initiator.

(First Solution)

Monomer m-1: 3.87 parts (31.3 mol %);

Monomer m-2: 7.46 parts (52.4 mol %);

Monomer m-3: 2.80 parts (16.3 mol %);

Ethyl lactate: 11.9 parts; and

Dimethyl-2,2′-azobisisobutylate: 1.243 parts (1.3 mol % based on thetotal feed amount of the monomers).

(Second Solution)

Monomer m-1: 23.34 parts (40 mol %);

Monomer m-2: 26.91 parts (40 mol %);

Monomer m-3: 16.20 parts (20 mol %);

Ethyl lactate: 98.9 parts; and

Dimethyl-2,2′-azobisisobutylate: 0.670 parts (0.7 mol % based on thetotal feed amount of the monomers).

The content ratio (polymer composition ratio) of the constitutionalunits of the polymer produced in each reaction time was determined bythe same procedures as in Reference Example 1. The results are shown inFIG. 5 and FIG. 13. The reaction time of the abscissa in FIG. 5 isreplaced with each cumulative polymerization (reaction) rate (%) toobtain a graph of FIG. 13.

Also, the weight-average molecular weight (Mw) and distribution ofmolecular weight (Mw/Mn) of the polymerization reaction solutionobtained by sampling at each reaction time were determined in the samemanner as in Reference Example 1. The results are shown in Table 5 andFIG. 6.

TABLE 5 Reaction time (hrs) Mw Mw/Mn 0.5 8600 1.82 1 8900 1.87 2 92001.84 3 9600 1.81 4 9800 1.83 5 9700 1.83 6 9500 1.85 7 9500 1.83

As shown by the results of FIG. 5, the polymer composition ratio becamealmost equal to the target composition ratio at any time just after thedropwise addition was started. A variation in polymer composition ratiocorresponding to the reaction time was also improved. This is the sameas the result of Example 1. Particularly, the polymer composition ratioof a polymer obtained until the reaction time is 4 hours by continuousdropwise addition differs a little from the target composition ratio.Also, as shown by the results of FIG. 13, the polymer composition ratiois almost equal to the target composition ratio at any time just afterthe start of the dropwise addition. Particularly, the polymercomposition ratio of a polymer obtained until the cumulativepolymerization (reaction) rate reaches 80% or more by continuousdropwise addition differs a little from the target composition ratio.

Also, as shown by the results of FIG. 6, there are small variations inweight-average molecular weight and distribution of molecular weightcorresponding to the reaction time just after the start of the dropwiseaddition until the end of the reaction.

(Refining of Polymer)

A polymer P2 was obtained from the polymerization reaction in the flaskjust after the reaction was continued for 7 hours. Mw and Mw/Mn of thepolymer P2 and the results of evaluation of solubility are shown inTable 10.

(Production of Resist Composition)

A resist composition containing the polymer P2 was prepared by the sameprocedures as in Example 1. Then, the sensitivity of the resistcomposition was evaluated. The results are shown in Table 10.

Reference Example 2 Design of First Composition Ratio

In this example, a first composition was determined in the case ofpolymerizing monomers m-4, m-5 and m-6 represented by the followingformulae (m-4), (m-5) and (m-6) respectively to produce a polymer sodesigned that its target composition ratio was m-4:m-5:m-6=40:40:20 (mol%) and its target value of molecular weight was 10,000.

The polymerization initiator used in the present invention wasdimethyl-2,2′-azobisisobutylate which was the same that was used inReference Example 1. The polymerization temperature was set to 80° C.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, a dropping funnel and a temperature gauge was charged with70.6 parts of propylene glycol monomethyl acetate (PGMEA) in a nitrogenatmosphere. The flask was bathed. Then, the bath temperature was raisedto 80° C. while stirring the content in the flask. Then, a droppingsolution (total amount: 220.612 g) containing the following monomermixture, solvent and polymerization initiator was prepared. Then, thissolution was added dropwise to the flask at a fixed dropping rate byusing the dropping funnel over 4 hours. Then, the flask was kept at 80°C. for 3 hours. After 7 hours passed since the dropwise addition of thedropping solution was started, the flask was cooled to ambienttemperature to stop the reaction.

Monomer m-4: 26.83 parts (40 mol %);

Monomer m-5: 40.25 parts (40 mol %);

Monomer m-6: 17.63 parts (20 mol %);

PGMEA: 127.1 parts; and

Dimethyl-2,2′-azobisisobutylate: 8.802 parts (8.9 mol % of the totalfeed amount of the monomers).

First, 0.5 g of the polymerization reaction solution was sampled at eachtime when 0.5, 1, 2, 3, 4, 5, 6 and 7 hours passed after the drop-wiseaddition of the above dropping solution was started. Then, the amountsof the monomers m-4 to m-6 were respectively measured quantitatively.Thus, the mass of each monomer left in the reactor is determined. As aresult, for example, the results obtained 1 hour and 2 hours after thedropwise addition is started are shown in Table 1.

TABLE 6 After 1 hr (parts by mass) After 2 hrs (parts by mass) Monomerm-4 2.60 2.62 Monomer m-5 2.84 2.89 Monomer m-6 0.96 0.98

Then, the mass of each monomer was converted into the mol ratio(corresponding to Mx:My:Mz) of each monomer left in the reactor at eachtime of sampling by using the molecular weight of each monomer.

As a result, for example, the results obtained 1 hour and 2 hours afterthe dropwise addition is started are shown in Table 7.

TABLE 7 After 1 hr (mol %) After 2 hrs (mol %) Monomer m-4 (Mx) 49.8049.46 Monomer m-5 (My) 36.17 36.39 Monomer m-6 (Mz) 14.03 14.15

On the other hand, the content ratio (polymer composition ratio,Px:Py:Pz) of the constitutional units in a polymer produced in eachreaction time was determined by the same procedures as in ReferenceExample 1. The results are shown in FIG. 7. The reaction time of theabscissa in FIG. 7 is replaced with each cumulative polymerization(reaction) rate (%) to obtain a graph of FIG. 14.

Also, the weight-average molecular weight (Mw) and distribution ofmolecular weight (Mw/Mn) of the polymerization reaction solutionobtained by sampling at each reaction time were determined. The resultsare shown in Table 8 and FIG. 8.

TABLE 8 Reaction time (hrs) Mw Mw/Mn 0.5 12800 2.17 1 12200 2.39 2 107002.29 3 9800 2.30 4 9400 2.23 5 9300 2.36 6 9300 2.43 7 9200 2.44

As shown by the results in FIG. 7, the polymer composition ratio(Px:Py:Pz) in a polymer produced 1 hour to 2 hours after the dropwiseaddition was started was closest to the target composition ratio40:40:20. The value of the polymer composition ratio was as follows:Px:Py:Pz=40.07:39.95:19.99.

Using this value and the value (Table 7) Mx:My:Mz obtained 2 hours afterthe dropwise addition was started, the factors Fx, Fy and Fz werecalculated according to Fx=Px/Mx, Fy=Py/My and Fz=Fz/Mz, to find thatFx=0.80, Fy=1.10, and Fz=1.42.

The above factor and target composition ratio were used to find a firstcomposition ratio x₀:y₀:z₀.

x₀=40/Fx=40/0.80=49.8 mol %

y₀=40/Fy=40/1.10=36.2 mol %

z0=20/Fz=20/1.42=14.0 mol %

(Calculation of W₀)

The ratio (W₀) occupied by the total mass (6.40 parts from Table 6) ofthe monomer existing in the reactor 1 hour after the start of thedropwise addition in a monomer mixture (total of 84.71 parts) containedin the first dropping solution is 7.6% by mass.

Example 3

In this example, a polymer was produced using the first compositionratio determined in Reference Example 2 by the above method (a)according to the present invention. The type of monomer, type ofpolymerization initiator, polymerization temperature, target compositionratio of the polymer and target value of the weight-average molecularweight in use are the same as those in Reference Example 2.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, two dropping funnels and a temperature gauge was charged withthe following first solution in a nitrogen atmosphere. The flask wasbathed. Then, the bath temperature was raised to 80° C. while stirringthe content in the flask.

Then, the following second solution was added dropwise to the flask byusing the dropping funnel over 4 hours. Then, the flask was kept at 80°C. for 3 hours. Also, the following polymerization initiator solutionwas added dropwise to the flask by using another dropping funnel for0.25 hours simultaneously with the start of the dropwise addition of thesecond solution. The flask was cooled to ambient temperature toterminate the reaction 7 hours after the dropwise addition of the secondsolution was started.

The ratio occupied by the monomer contained in the first solution basedon the total feed amount of the monomer was set to 7.6% by massaccording to W₀ in Reference Example 2.

In this example, the standard time is 4 hours. Also, the high-ratefeeding period is the period (0.25 hours) during which thepolymerization initiator solution was added dropwise. Specifically, thehigh-rate feeding period (0 to j %) is 0 to 6.25% (j=6.25%) of thestandard time. The polymerization initiator to be fed to the reactorduring high-rate feeding period is about 55% by mass of the total feedamount of the polymerization initiator.

(First Solution)

Monomer m-4: 2.60 parts (49.8 mol %);

Monomer m-5: 2.84 parts (36.2 mol %);

Monomer m-6: 0.96 parts (14.0 mol %); and

PGMEA: 80.2 parts.

(Second Solution)

Monomer m-4: 24.80 parts (40 mol %);

Monomer m-5: 37.21 parts (40 mol %);

Monomer m-6: 16.30 parts (20 mol %);

PGMEA: 110.0 parts; and

Dimethyl-2,2′-azobisisobutylate: 3.456 parts (3.49 mol % based on thetotal feed amount of the monomers).

(Polymerization Initiator Solution)

PGMEA: 7.5 parts; and

Dimethyl-2,2′-azobisisobutylate: 4.224 parts (4.26 mol % based on thetotal feed amount of the monomers)

The content ratio (polymer composition ratio) of the constitutionalunits of a polymer produced in each reaction time was determined. Theresults are shown in FIG. 9. The reaction time of the abscissa in FIG. 9is replaced with each cumulative polymerization (reaction) rate (%) toobtain a graph of FIG. 15.

Also, the weight-average molecular weight (Mw) and distribution ofmolecular weight (Mw/Mn) of the polymerization reaction solutionobtained by sampling at each reaction time were determined in the samemanner as in Reference Example 2. The results are shown in Table 9 andFIG. 10.

TABLE 9 Reaction time (hrs) Mw Mw/Mn 0.5 9600 2.31 1 9100 2.19 2 88002.21 3 8900 2.18 4 9100 2.18 5 9000 2.27 6 9000 2.30 7 9000 2.32

The results shown in FIG. 7 and FIG. 9 are compared. In ReferenceExample 2 (FIG. 7), the polymer composition ratio of a polymer producedjust after the dropwise addition was started largely deviates from thetarget composition ratio. Also, there is a large variation in polymercomposition ratio according to the reaction time.

In Example 3 (FIG. 9) in which the flask was charged with the firstsolution in advance, the polymer composition ratio was, on the otherhand, almost equal to the target composition ratio at any time justafter the dropwise addition was started. A variation in compositionratio corresponding to the reaction time was also improved.Particularly, the polymer composition ratio of a polymer obtained untilthe reaction time is 4 hours by continuous dropwise addition differs alittle from the target composition of ratio.

The results of FIG. 14 and FIG. 15 are compared with each other. InReference Example 2 (FIG. 14), the polymer composition ratio of apolymer produced just after the start of the dropwise addition largelydeviates from the target composition ratio from the viewpoint ofcumulative polymerization (reaction) rate (%). Also, there is a largevariation in polymer composition ratio.

In Example 3 (FIG. 15) in which the flask is charged with the firstsolution in advance, the polymer composition ratio is almost equal tothe target composition ratio at any time just after the start of thedropwise addition. Particularly, the polymer composition ratio of apolymer obtained until the cumulative polymerization (reaction) ratereaches 80% or more by continuous dropwise addition differs a littlefrom the target composition ratio.

Also, the results of FIG. 8 and FIG. 10 are compared. In Reference 2(FIG. 8), particularly, the weight-average molecular weight obtained 3hours after the start of the dropwise addition largely differs from thatof a polymer obtained after that time. Also, there is a large variationcorresponding to the reaction time.

In Example 3 (FIG. 10), on the other hand, there are small variations inweight-average molecular weight and distribution of molecular weightcorresponding to the reaction time just after the start of the dropwiseaddition until the end of the reaction.

(Refining of a Polymer)

The mixture solvent of methanol and water (methanol/water=80/20 volumeratio) and (methanol/water=90/10 volume ratio) were altered to a mixturesolvent of methanol and water (methanol/water=90/10 volume ratio) and(methanol/water=95/5 volume ratio) respectively. A polymer P3 wasobtained from the polymerization reaction solution in the flask afterthe reaction was continued for 7 hours by the same procedures as inExample 1 except for the above alteration. Mw and Mw/Mn, and also thesolubility of the polymer P3 were evaluated. The results are shown inTable 10.

(Production of a Resist Composition)

A resist composition containing the polymer P3 was prepared by the sameprocedures as in Example 1. Then, the sensitivity of the resistcomposition was evaluated. The results are shown in Table 10.

Comparative Example 1

In Reference Example 1, the flask was cooled to ambient temperature tostop the reaction after the reaction was continued for 7 hours. Acomparative polymer 1 was obtained using the obtained polymerizationreaction solution in the flask by the same procedures as in the polymerrefining step of Example 1. With regard to the comparative polymer 1,its Mw and Mw/Mn were determined and also, its solubility was evaluated.

Also, a resist composition was prepared using the comparative polymer 1by the same procedures as in Example 1. Then, the sensitivity of theresist composition was evaluated. The results are shown in Table 10.

Comparative Example 2

In Reference Example 2, the flask was cooled to ambient temperature tostop the reaction after the reaction was continued for 7 hours. Acomparative polymer 2 was obtained using the obtained polymerizationreaction solution in the flask by the same procedures as in the polymerrefining step of Example 3. With regard to the comparative polymer 2,its Mw and Mw/Mn were determined and also, its solubility was evaluated.

Also, a resist composition was prepared using the comparative polymer 2by the same procedures as in Example 3. Then, the sensitivity of theresist composition was evaluated. The results are shown in Table 10.

TABLE 10 Evaluation results solubility sensitivity Mw Mw/Mn (min)(mJ/cm²) Example 1 10000 1.66 15 1.04 Example 2 9900 1.65 15 1.10Comparative 10600 1.68 31 1.65 Example 1 Example 3 9600 1.74 16 1.05Comparative 9800 1.86 38 1.41 Example 2

From the results of Table 10, the solubility of each polymer obtained inExamples 1, 2 and 3 was significantly improved in each polymer obtainedin Comparative Examples 1 and 2. Also, the sensitivity of the resistcomposition containing the polymer obtained in Example 1, 2 or 3 wasmore improved than that of the resist composition containing the polymerobtained in Comparative Example 1 or 2.

Example 4 and Comparative Example 3

Monomers (m-1), (m-7) and (m-8) used in the synthesis of the followingcopolymers C-1 and C-2 are shown below.

Comparative Example 3

A copolymer C-1 was synthesized in the following synthetic procedures.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, two dropping funnels and a temperature gauge was charged with56.5 parts of PGME in a nitrogen atmosphere. The flask was bathed. Then,the bath temperature was raised to 80° C. while stirring the content inthe flask.

Then, a dropping solution (total amount: 173.3 g) containing thefollowing monomer mixture, a solvent and a polymerization initiator wasprepared. Then, the solution was added dropwise at a fixed dropping ratein the flask by using the dropping funnel over 4 hours. Then, the flaskwas kept at 80° C. for 3 hours. The flask was cooled to ambienttemperature to terminate the reaction 7 hours after the dropwiseaddition of the second solution was started.

Monomer m-1: 18.7 parts (24.4 mol %);

Monomer m-7: 18.7 parts (23.5 mol %);

Monomer m-8: 30.5 parts (52.1 mol %); and

PGME: 101.7 parts.

2,2′-azobisisobutyronitrile: 3.7 parts (5.0 mol % based on the totalfeed amount of the monomers).

Example 4

A copolymer C-2 was synthesized in the following synthetic procedures.

In this case, the following factors Fx, Fy and Fz were determined by thesame procedures as in Reference Example 1 in the case where the targetcomposition ratio (mol %) (m-1):(m-7):(m-8)=24.4:23.5:52.1. As a result,each factor was as follows: Fx(m-1)=1.17, Fy(m-7)=0.84, and Fz(m-8)=1.02.

Using these factors and the above target composition ratio, the firstcomposition ratio x₀:y₀:z₀ and the total mass (W₀) of the monomersexisting in the reactor were determined.

x_(0(m-1))=20.9 mol %

y_(0(m-7))=28.0 mol %

z_(0(m-8))=51.1 mol %

(Calculation of W₀)

The ratio (W₀) occupied by the total mass (6.40 parts from Table 6) ofthe monomers existing in the reactor 1 hour after the start of thedropwise addition in a monomer mixture was as follows: W₀=10.1% by mass.

(First Solution)

Monomer m-1: 1.8 parts (20.9 mol %);

Monomer m-7: 2.5 parts (28.0 mol %);

Monomer m-8: 3.3 parts (51.1 mol %); and

PGME (propylene glycol monomethyl ether): 56.5 parts.

(Second Solution)

Monomer m-1: 18.7 parts (24.4 mol %);

Monomer m-7: 18.7 parts (23.5 mol %);

Monomer m-8: 30.5 parts (52.1 mol %); and

PGME (propylene glycol monomethyl ether): 101.7 parts.

2,2′-azobisisobutyronitrile: 3.48 parts (4.24 mol % based on the totalfeed amount of the monomers).

(Polymerization Initiator Solution)

PGME (propylene glycol monomethyl ether): 17.7 parts; and

2,2′-azobisisobutyronitrile: 0.87 parts (1.06 mol % based on the totalfeed amount of the monomers)

<Synthesis of Copolymer C-2>

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, two dropping funnels and a temperature gauge was charged withthe mixture solution prepared in the above mixing ratio of the firstsolution in a nitrogen atmosphere. Then, the bath temperature was raisedto 80° C. while stirring the content in the flask.

Then, the mixture solution prepared in the above mixing ratio of thesecond solution was added dropwise at a fixed dropping rate in the flaskby using the dropping funnel over 6 hours. Then, the flask was kept at80° C. for 1 hour.

The mixture solution prepared in the above mixing ratio of thepolymerization initiator solution was added dropwise to the flask byusing another dropping funnel over 0.5 hours simultaneously with thestart of the dropwise addition of the mixture solution of the secondsolution. In this case, the weight-average molecular weight of acopolymer produced in the initial stage of the polymerization stepvaries corresponding to the amount of the polymerization initiator to beadded dropwise to this step. However, it is designed so that theweight-average molecular weight is close to the target polymerizationaverage molecular weight of each copolymer.

Then, IPE (diisopropyl ether) was prepared in an amount about 7 timesthat of the obtained reaction solution. Then, the reaction solution wasadded dropwise to the prepared IPE while stirring to obtain a whitegel-like precipitate. Then, the obtained precipitate was separated byfiltration.

Then, IPE (diisopropyl ether) was prepared in the same amount as thatprepared in the above step. Then, the separated precipitate was pouredinto this mixture solvent. The precipitate was separated by filtrationand recovered. Then, the precipitate was dried at 60° C. under reducedpressure for about 40 hours to obtain a powder of each copolymer.

(Weight-Average Molecular Weight of Copolymer for Lithography)

The weight-average molecular weight (Mw) and distribution of molecularweight (Mw/Mn) of each of the obtained copolymers C-1 and C-2 weremeasured in the following methods.

About 20 mg of a sample was dissolved in 5 mL of THF. Then, the solutionwas filtered through a 0.5-μm membrane filter to prepare a samplesolution. Then, this sample solution was subjected to a gel permeationchromatography (GPC) apparatus (trade name: HCL-8220, manufactured byTosoh Co., Ltd.) used to measure the weight-average molecular weight(Mw) and number-average molecular weight (Mn) and also the distributionof molecular weight (Mw/Mn). In this measurement, a column prepared byconnecting three columns (trade name: Shodex GPC K-804 L, manufacturedby Showa Denko K.K.) in series was used as the separation column. Also,THF (tetrahydrofuran) was used as a solvent. The flow rate was set to1.0 mL/min. Also, a differential reflectometer was used as a detector.The measuring temperature was set to 40° C. Also, the amount of thesample solution to be injected was set to 0.1 mL. In addition,polystyrene was used as the standard polymer. The results of themeasurement are shown in Table 11.

TABLE 11 Solubility Mw/ Transparency Mw Mn (%) Comparative Copolymer9700 1.80 87 Example 3 C-1 Example 4 Copolymer 9500 1.73 99 C-2(Evaluation of Solubility)

The copolymers C-1 and C-2 for lithography were respectively used toprepare a solution for evaluating solubility. The temperature of thesolution was set to ambient temperature (25° C.). As anultraviolet-visible absorptiometer, UV-3100 PC (trade name),manufactured by Shimadzu Corporation was used. The solution formeasurement was placed in a quartz cuvette having an optical path lengthof 10 mm. The solubility was evaluated by a method of measuringtransmittance having a wavelength of 450 nm. The higher thetransmittance is, the better the solubility is. Also, a variation inlithographic performance in plane that is caused when the copolymer isapplied to the substrate is more reduced with an increase in the abovetransmittance. The results are shown in Table 11.

(Preparation of Solution Used to Evaluate Solubility)

The following ingredients were blended to obtain a solution forevaluation.

Copolymer for lithography: 2.5 parts

Solvent 1 (PGME): 100 parts

Solvent 2 (IPE): 16 parts

As shown by the results of Table 11, the value of the transmittanceshowing solubility ascends in the order of Copolymers 1 and 2. Thisconfirmed that the lithographic performance of the copolymer C-2(Example 4) produced by the production method of the present inventionwas superior to that of the copolymer C-1 (Comparative Example 3).

Copolymer for Lithography Examples 5 to 7 and Comparative Examples 4 to6

In Examples 5 to 7 and Comparative Examples 4 to 6, the followingmeasuring methods and evaluation methods were used.

(Measurement of Weight-Average Molecular Weight)

The weight-average molecular weight (Mw) and distribution of molecularweight (Mw/Mn) of the polymer was determined as a value based onpolystyrene by GPC under the following conditions (GPC condition).

(GPC Condition)

Apparatus: Tosoh High-Performance GPC apparatus (trade name),manufactured by Tosoh Co., Ltd.;

Separation column: column prepared by connecting three columns (tradename: Shodex GPC K-805 L, manufactured by Showa Denko K.K.) in series;

Measuring temperature: 40° C.;

Eluent: THF;

Sample: Solution obtained by dissolving about 20 mg of the copolymer in5 mL of THF, and by filtering the solution by a 0.5-μm membrane filter;

Flow rate: 1 mL/min;

Injection amount: 0.1 mL

Detector: Differential reflectometer.

Calibration curve I: about 20 mg of standard polystyrene was dissolvedin 5 mL of THF. Then, the solution was filtered through a 0.5-μmmembrane filter. This solution was injected into the separation columnin the above condition. Then, the relationship between the elution timeand the molecular weight was determined. The following standardpolystyrenes (all names are trade names) manufactured by Tosoh Co., Ltd.were each used as the standard polystyrene.

F-80 (Mw=706,000);

F-20 (Mw=190,000);

F-4 (Mw=37,900);

F-1 (Mw=10,200);

A-2500 (Mw=2,630),

A-500 (mixture of products: Mw=682, 578, 474, 370 and 260)

(Measurement of Average Monomer Composition of Copolymer)

About 5 parts by mass of the copolymer was dissolved in about 95 partsby mass of deuterated dimethyl sulfoxide to obtain a sample solution.This sample solution was placed in a NMR tube. Then, the sample solutionwas analyzed using ¹H-NMR (manufactured by JEOL Ltd., resonancefrequency: 270 MHz). The monomer composition ratio of the copolymer wascalculated from the integral intensity ratio of signals derived fromeach constitutional unit.

(Division of Copolymer by GPC)

The copolymer was divided by GPC under the following conditions (GPCcondition). Also, a solvent was distilled from a fraction solution firsteluted to obtain a solid. This is a polymer having the highest molecularweight.

(GPC Condition)

Apparatus: Preparative LC (trade name: LC-9105, Japan AnalyticalIndustry Co., Ltd.);

Separation column: column obtained by connecting JAIGEL-2H and JAIGEL-3H(trade name), manufactured by Japan Analytical Industry Co., Ltd. inseries;

Measuring temperature: 40° C.;

Eluent: THF

Sample: Solution obtained by dissolving about 1 g of the copolymer in 10mL of THF, and by filtering the solution by a 0.5-μm membrane filter;

Flow rate: 1 mL/min;

Injection amount: 0.1 mL

Detector: Ultraviolet-visible absorptiometer and differentialreflectometer.

Preparative method: Prepared by dividing an eluate showing peaksoriginated from the copolymer in an elution curve, into 8 fractions inorder of elution such that each fraction has the same volume.

(Measurement of Fractionated Monomer Composition Ratio)

A fractionated monomer composition ratio in a high-molecular-weightfraction, which was first eluted among eight fractions prepared in theabove method, was measured in the following method.

About 5 parts by mass of a solid obtained by distilling a solvent fromthe first eluted high-molecular-weight fraction was dissolved in about95 parts by mass of deuterated dimethyl sulfoxide to prepare a samplesolution. This sample solution was placed in a NMR tube. Then, thesample solution was analyzed using ¹H-NMR (manufactured by JEOL Ltd.,resonance frequency: 270 MHz). The monomer composition ratio of thecopolymer was calculated from the integral intensity ratio of signalsderived from each constitutional unit.

(Evaluation of the Solubility of the Copolymer)

20 parts of the copolymer and 80 parts of PGMEA were blended with eachother. Then, the time taken to completely dissolve the copolymer wasmeasured while stirring the mixture at 25° C. It was visually determinedwhether the copolymer was completely dissolved or not.

(Evaluation of the Sensitivity of the Resist Composition)

The resist composition was applied to a 6-inch silicon wafer withrotation. Then, the wafer was prebaked (PAB) at 120° C. on a hot platefor 60 seconds to form a resist film 300 nm in thickness. Using an ArFexcimer laser exposure apparatus (trade name: VUVES-4500, manufacturedby Litho Tech Japan Corporation), 18 shots having an area of 10 mm×10 mmwere exposed to light at varied doses. Then, the resist film waspost-baked (PEB) at 110° C. for 60 seconds. After that, using a resistdeveloping analyzer (trade name: RDA-806, manufactured by Litho TechJapan Corporation), the resist film was developed at 23.5° C. by anaqueous 2.38% tetramethylammonium solution for 65 seconds. The resistfilm exposed at each dose was measured to detect a variation in resistfilm thickness with time during developing.

The relationship between the logarithm of the exposure dose(unit:mJ/cm²) and the proportion (unit:%, hereinafter referred to as aresidual film ratio) of a residual film thickness with respect to theinitial film thickness when the resist film was developed for 30 secondswas plotted based on the obtained data of the variation in filmthickness with time, to make a dose-residual film ratio curve. Based onthis curve, the value of the exposure dose (Eth) required to reduce theresidual film ratio to 0% was determined. Specifically, the exposuredose (mJ/cm²) at the point where the dose-residual film ratio curvecrosses a line of 0% residual film ratio was determined as Eth. This Ethvalue indicates the sensitivity of the resist composition. As this valuebecomes smaller, the sensitivity of the resist composition becomeshigher.

Example 5 Production of a Copolymer

In this example, the following monomers (m′-1), (m′-2) and (m′-3) werepolymerized.

A flask equipped with a nitrogen introduction port, a stirrer, acondenser, a dropping funnel and a temperature gauge was charged withthe following first solution in a nitrogen atmosphere. The flask wasbathed. Then, the bath temperature was raised to 80° C. while stirringthe content in the flask.

Then, the following polymerization initiator solution was added dropwiseat a fixed rate in the flask from a dropping machine over 0.25 hours.The following second solution was added dropwise at a fixed rate from adropping machine over 4 hours simultaneously with the start of thedropwise addition of the polymerization initiator. Then, the flask waskept at 80° C. for 3 hours.

The polymerization initiator to be fed to the reactor during a period(high-rate feeding period) in which the polymerization initiator isadded dropwise is about 65% by mass of the total feed amount of thepolymerization initiator.

(First Solution)

Monomer m′-1: 2.72 parts (32.26 mol %);

Monomer m′-2: 4.90 parts (50.48 mol %);

Monomer m′-3: 2.02 parts (17.26 mol %); and

Ethyl lactate: 79.0 parts.

(Second Solution)

Monomer m′-1: 23.80 parts (40.00 mol %);

Monomer m′-2: 27.44 parts (40.00 mol %);

Monomer m′-3: 16.52 parts (20.00 mol %);

Ethyl lactate: 98.06 parts; and

Dimethyl-2,2′-azobisisobutylate (trade name: V601, manufactured by WakoPure Chemical Industries Ltd., the same as follows): 0.643 parts (0.700mol % based on the total feed amount of the monomers).

(Polymerization Initiator Solution)

Ethyl lactate: 3.6 parts; and

Dimethyl-2,2′-azobisisobutylate: 1.196 parts (1.301 mol % based on thetotal feed amount of the monomers)

Then, the polymerization reaction solution in the flask was addeddropwise to a mixture solvent of methanol and water(methanol/water=80/20 ratio by volume) having a volume ten times that ofthe reaction solution while stirring to obtain a white precipitate(copolymer A-1). The precipitate was separated by filtration. Then, theseparated precipitate was again poured into a mixture solvent ofmethanol and water (methanol/water=90/10 ratio by volume) having thesame amount as above. Then, the mixture was washed while stirring. Then,the washed precipitate was separated by filtration to obtain a wetpolymer powder. The wet polymer powder was dried at 40° C. under reducedpressure for about 40 hours to obtain a white powder (66.0 g).

The obtained white powder was analyzed by ¹H-NMR and GPC to find theaverage monomer composition, Mw and Mw/Mn of all copolymers.

Mw and Mw/Mn of the obtained copolymer A-1, the content ratio of eachmonomer in each of the average monomer composition and the fractionatedmonomer composition, and with regard to each monomer, a differenceobtained by subtracting the content ratio of the average monomercomposition from the content ratio of the fractionated monomercomposition are shown in Table 12.

Also, the solubility of the obtained copolymer A-1 was evaluated by theabove method. The results are shown in Table 12.

(Production of a Resist Composition)

2 parts of triphenylsulfonium triflate as a photoacid generator and 700parts of PGMEA as a solvent were blended with 100 parts of the obtainedcopolymer A-1 to obtain a homogeneous solution. Then, this solution wasfiltered through a membrane filter having a pore size of 0.1 μm toprepare a resist composition solution. The sensitivity of the obtainedresist composition was evaluated by the above method. The results areshown in Table 12.

Example 6

In this example, the following monomers (m′-4), (m′-5) and (m′-6) werepolymerized.

The same flask that was used in Example 5 was charged with the followingfirst solution in a nitrogen atmosphere. The flask was bathed. Then, thebath temperature was raised to 80° C. while stirring the content in theflask.

Then, the following polymerization initiator solution was added dropwiseat a fixed rate in the flask from a dropping machine over 0.25 hours.The following second solution was added dropwise at a fixed rate from adropping machine over 4 hours simultaneously with the start of thedropwise addition of the polymerization initiator. Then, the flask waskept at 80° C. for 3 hours.

In this example, the polymerization initiator to be fed to the reactorduring a period (high-rate feeding period) in which the polymerizationinitiator is added dropwise is about 50% by mass of the total feedamount of the polymerization initiator.

(First Solution)

Monomer m′-4: 2.72 parts (49.40 mol %);

Monomer m′-5: 2.88 parts (33.99 mol %);

Monomer m′-6: 1.27 parts (16.61 mol %); and

PGMEA: 71.8 parts.

(Second Solution)

Monomer m′-4: 30.60 parts (55.56 mol %);

Monomer m′-5: 18.86 parts (22.22 mol %);

Monomer m′-6: 16.99 parts (22.22 mol %);

PGMEA: 96.1 parts; and

Dimethyl-2,2′-azobisisobutylate: 2.422 parts (2.955 mol % based on thetotal feed amount of the monomers).

(Polymerization Initiator Solution)

PGMEA: 3.6 parts; and

Dimethyl-2,2′-azobisisobutylate: 2.422 parts (2.955 mol % based on thetotal feed amount of the monomers)

Then, the polymerization reaction solution in the flask was addeddropwise to a mixture solvent of methanol and water(methanol/water=85/15 ratio by volume) having a volume ten times that ofthe reaction solution while stirring to obtain a white precipitate(copolymer A-2). The precipitate was separated by filtration. Then, theseparated precipitate was again poured into a mixture solvent ofmethanol and water (methanol/water=9/1 ratio by volume) having the sameamount as above. Then, the mixture was washed while stirring. Then, thewashed precipitate was separated by filtration to obtain a wet polymerpowder. The wet polymer powder was dried at 40° C. under reducedpressure for about 40 hours to obtain a white powder (63.0 g).

The obtained white powder was measured and evaluated by the sameprocedures as in Example 5. The results are shown in Table 12.

Example 7

In this example, the following monomers (m′-7), (m′-8) and (m′-9) werepolymerized.

The same flask that was used in Example 5 was charged with the followingfirst solution in a nitrogen atmosphere. The flask was bathed. Then, thebath temperature was raised to 80° C. while stirring the content in theflask.

Then, the following polymerization initiator solution was added dropwiseat a fixed rate in the flask from a dropping machine over 0.25 hours.The following second solution was added dropwise at a fixed rate from adropping machine over 4 hours simultaneously with the start of thedropwise addition of the polymerization initiator. Then, the flask waskept at 80° C. for 3 hours.

In this example, the polymerization initiator to be fed to the reactorduring a period (high-rate feeding period) in which the polymerizationinitiator is added dropwise is about 60% by mass of the total feedamount of the polymerization initiator.

(First Solution)

Monomer m′-7: 1.70 parts (17.92 mol %);

Monomer m′-8: 10.42 parts (75.34 mol %);

Monomer m′-9: 0.89 parts (6.74 mol %);

Ethyl lactate: 57.3 parts; and

PGMEA: 26.2 parts.

(Second Solution)

Monomer m′-7: 20.23 parts (41.17 mol %);

Monomer m′-8: 29.51 parts (41.17 mol %);

Monomer m′-9: 12.04 parts (17.66 mol %);

Ethyl lactate: 57.2 parts;

PGMEA: 30.8 parts; and

Dimethyl-2,2′-azobisisobutylate: 1.744 parts (2.199 mol % based on thetotal feed amount of the monomers).

(Polymerization Initiator Solution)

Ethyl lactate: 7.7 parts; and

Dimethyl-2,2′-azobisisobutylate: 2.569 parts (3.239 mol % based on thetotal feed amount of the monomers)

Then, the polymerization reaction solution in the flask was addeddropwise to a mixture solvent of methanol and water(methanol/water=85/15 ratio by volume) having a volume ten times that ofthe reaction solution while stirring to obtain a white precipitate(copolymer A-3). Then, the precipitate was separated by filtration.Then, the separated precipitate was again poured into a mixture solventof methanol and water (methanol/water=95/5 ratio by volume) having thesame amount as above. Then, the mixture was washed while stirring. Then,the washed precipitate was separated by filtration to obtain a wetpolymer powder. The wet polymer powder was dried at 40° C. under reducedpressure for about 40 hours to obtain a white powder (58.0 g).

The obtained copolymer A-3 was measured and evaluated by the sameprocedures as in Example 5. The results are shown in Table 12.

Comparative Example 4

In Example 5, a copolymer was synthesized without any monomer existingin advance in the flask. The molar ratio of the monomers used in thisexample is as follows: (m′-1):(m′-2):(m′-3)=40.00:40.00:20.00.

Specifically, the same flask that was used in Example 5 was charged with64.5 parts of ethyl lactate in a nitrogen atmosphere. The flask wasbathed. Then, the temperature of the bath was raised to 80° C. whilestirring the content in the flask.

A solution containing 27.20 parts of the monomer (m′-1), 31.36 parts ofthe monomer (m′-2), 18.88 parts of the monomer (m′-3), 112.6 parts ofethyl lactate, and 2.576 parts of dimethyl-2,2′-azobisisobutylate (tradename: V601 mentioned above) was added dropwise at a fixed rate over 4hours in the flask from a dropping machine containing the solution. Theflask was kept at 80° C. for 3 hours.

After that, a white precipitate (copolymer B-1) was obtained by the sameprocedures as in Example 5. The precipitate was then separated byfiltration. Then, the separated precipitate was washed. After beingwashed, the precipitate was separated by filtration. The obtainedprecipitate was dried to obtain a white powder (64.0 g).

The obtained copolymer B-1 was measured and evaluated by the sameprocedures as in Example 5. The results are shown in Table 12.

Comparative Example 5

In Example 6, a copolymer was synthesized without any monomer existingin advance in the flask. The molar ratio of the monomers used in thisexample is as follows: (m′-4): (m′-5): (m′-6)=55.56:22.22:22.22.

Specifically, the same flask that was used in Example 5 was charged with61.5 parts of PGMEA in a nitrogen atmosphere. The flask was bathed.Then, the temperature of the bath was raised to 80° C. while stirringthe content in the flask.

A solution containing 34.00 parts of the monomer (m′-4), 20.96 parts ofthe monomer (m′-5), 18.88 parts of the monomer (m′-6), 110.76 parts ofPGMEA, and 8.197 parts of dimethyl-2,2′-azobisisobutylate (trade name:V601 mentioned above) was added dropwise at a fixed rate over 4 hours inthe flask from a dropping machine containing the solution. The flask waskept at 80° C. for 3 hours.

After that, a white precipitate (copolymer B-2) was obtained by the sameprocedures as in Example 6. The precipitate was then separated byfiltration. Then, the separated precipitate was washed. After beingwashed, the precipitate was separated by filtration. The obtainedprecipitate was dried to obtain a white powder (63.0 g).

The obtained copolymer B-2 was measured and evaluated by the sameprocedures as in Example 5. The results are shown in Table 12.

Comparative Example 6

In Example 7, a copolymer was synthesized without any monomer existingin advance in the flask. The molar ratio of the monomers used in thisexample is as follows: (m′-7):(m′-8):(m′-9)=41.17:41.17:17.66.

Specifically, the same flask that was used in Example 5 was charged with42.4 parts of ethyl lactate, 18.2 parts of PGMEA in a nitrogenatmosphere. The flask was bathed. Then, the temperature of the bath wasraised to 80° C. while stirring the content in the flask.

A solution containing 23.80 parts of the monomer (m′-7), 34.72 parts ofthe monomer (m′-8), 14.16 parts of the monomer (m′-9), 76.3 parts ofethyl lactate, 32.7 parts of PGMEA, and 5.083 parts ofdimethyl-2,2′-azobisisobutylate (trade name: V601 mentioned above) wasadded dropwise at a fixed rate over 4 hours in the flask from a droppingmachine containing the solution. The flask was kept at 80° C. for 3hours.

After that, a white precipitate (copolymer B-3) was obtained by the sameprocedures as in Example 7. The precipitate was then separated byfiltration. Then, the separated precipitate was washed. After beingwashed, the precipitate was separated by filtration. The obtainedprecipitate was dried to obtain a white powder (57.0 g).

The obtained copolymer B-3 was measured and evaluated by the sameprocedures as in Example 5. The results are shown in Table 12.

TABLE 12 Example Comparative Example Copolymer A-1 A-2 A-3 B-1 B-2 B-3Weight-average molecular weight (Mw) 10500 9600 6500 10600 9800 7400Molecular weight distribution 1.59 1.58 1.55 1.64 1.70 1.60 Contentratio m′-1 Average monomer 40.1 40.7 (mol %) of composition ratioconstitutional Fraction monomer 39.2 43.0 units in monomer compositionratio composition Difference (fraction − −0.9 2.3 average) ratio m′-2Average monomer 40.3 35.5 composition ratio Fraction monomer 40.7 38.9composition ratio Difference (fraction − 0.4 3.4 average) ratio m′-3Average monomer 19.2 20.4 composition ratio Fraction monomer 20.5 21.5composition ratio Difference (fraction − 1.3 1.1 average) ratio m′-4Average monomer 59.6 58.0 composition ratio Fraction monomer 58.3 61.0composition ratio Difference (fraction − −1.3 3.0 average) ratio m′-5Average monomer 22.4 21.2 composition ratio Fraction monomer 20.4 17.4composition ratio Difference (fraction − −2.0 −3.8 average) ratio m′-6Average monomer 20.5 22.3 composition ratio Fraction monomer 21.2 21.6composition ratio Difference (fraction − 0.7 −0.7 average) ratio m′-7Average monomer 38.2 41.8 composition ratio Fraction monomer 39.0 44.0composition ratio Difference (fraction − 0.8 2.2 average) ratio m′-8Average monomer 44.1 39.5 composition ratio Fraction monomer 41.7 36.4composition ratio Difference (fraction − −2.4 −3.1 average) ratio m′-9Average monomer 17.7 18.7 composition ratio Fraction monomer 20.3 22.8composition ratio Difference (fraction − 2.6 4.1 average) ratioSolubility (min) 17 25 12 31 38 18 Sensitivity (mJ/cm²) 1.32 2.23 0.541.61 2.89 0.79

As is shown by the results in Table 12, the weight-average molecularweight of the copolymer A-1 obtained in Example 5 is almost equal to theweight-average molecular weight of the copolymer B-1 obtained inComparative Example 1. However, the distribution of molecular weight ofA-1 is smaller than that of B-1. Also, in the case of A-1, thedifference between the fractionated monomer composition ratio and theaverage monomer composition ratio is in a range from −3 mol % to +3 mol%. This fits to any of the constitutional units derived from themonomers (m′-1), (m′-2) and (m′-3). With regard to the copolymer B-1, onthe other hand, the difference between the fractionated monomercomposition ratio and average monomer composition ratio of a part of theconstitutional units exceeds the range from −3 mol % to +3 mol %. Also,the copolymer A-1 is outstandingly superior to the copolymer B-1 insolubility and sensitivity.

Also, the same tendency is determined in the case of comparing thecopolymer A-2 obtained in Example 6 with the copolymer B-2 obtained inComparative Example 5 and also in the case of comparing the copolymerA-3 obtained in Example 7 with the copolymer B-3 obtained in ComparativeExample 6.

INDUSTRIAL APPLICABILITY

The present invention can provide a method for producing a polymer whichcan improve a variation in the content ratio of constitutionalcomponents and in molecular weight in a copolymer, and also insolubility in a solvent and in sensitivity when used for a resistcomposition, a polymer obtained by the above production method and usedfor lithography, and a resist composition containing the polymer usedfor lithography and a method for producing a substrate with a patternformed thereon by using the resist composition.

DESCRIPTION OF REFERENCE SIGNS

-   B Baseline-   S Peak start-   E Peak end

The invention claimed is:
 1. A polymerization method, the methodcomprising: (I) feeding a first solution to a reactor, wherein thefeeding (I) occurs before or simultaneously with the start of a dropwiseaddition of a polymerization initiator to the reactor, and the firstsolution comprises two or more monomers α₁ to α_(n) in a firstcomposition ratio; (II) feeding a second solution to the reactor,wherein the feeding (II) occurs after or simultaneously with the startof the feeding (I) of the first solution, wherein: n denotes an integerof 2 or more; the monomers α₁ to α_(n) are polymerized while themonomers α₁ to α_(n) and the polymerization initiator are added dropwiseto the reactor to obtain a copolymer comprising constitutional units α′₁to α′_(n), wherein α′₁ to α′_(n) represent constitutional units derivedfrom the monomers α₁ to α_(n); the first composition ratio is such thatthe monomers α₁ to α_(n) are reacted in a steady state based onrespective reaction rates of the monomers α₁ to α_(n); when a targetcomposition ratio (in mol %), which is represented by a constant ratioof the constitutional units α′₁ to α′_(n), of the copolymer is α′₁:α′₂:. . . :α′_(n), the second solution comprises the monomers α₁ to α_(n)having the same composition ratio as the target composition ratio, andwherein the first composition ratio is determined by: (i) addingdropwise at a fixed dropping rate, to a reactor containing a solvent, adropping solution comprising 100 parts by mass of a monomer mixturehaving the same monomer composition ratio as the target compositionratio, α′₁:α′₂: . . . :α′_(n), the polymerization initiator; and thesolvent, wherein a composition ratio (in mol %) M₁:M₂: . . . :M_(n) ofthe monomers α₁ to α_(n) remaining in the reactor is calculated when apassage of time from the start of the dropwise addition is t₁, t₂, t₃ .. . , and t_(m), and a ratio (in mol %) P₁:P₂: . . . :P_(n) of theconstitutional units α′₁ to α′_(n) of each polymer formed, between thetime t₁ to the time t₂, time t₂ to the time t₃, . . . , and time t_(m)to the time t_(m+1) is calculated; (ii) determining a time zone fromt_(m) to t_(m+1) when the ratio P₁:P₂: . . . :P_(n) becomes nearest tothe target composition ratio α′₁:α′₂: . . . :α′_(n), wherein mrepresents an integer of 1 or more; and (iii) determining factors F₁,F₂, . . . , and F_(n) from the value of the ratio P₁:P₂: . . . :P_(n)between t_(m) and t_(m+1) and the value of the composition ratio M₁:M₂:. . . :M_(n) at the passage of time t_(m) based on equations F₁=P₁/M₁,F₂=P₂/M₂, . . . , and Fn=P_(n)/M_(n), wherein:α₁=α′ ₁/F₁, α₂=α′₂/F₂, . .. , α_(n)=α′_(n)/F_(n); and (III) feeding the polymerization initiatorto the reactor, wherein the polymerization initiator is added dropwiseat a rate higher than an average feed rate Vj during a high-rate feedingperiod which occurs at an early stage of the polymerization, the averagefeed rate Vj is defined as a value obtained by dividing a total feedamount of the polymerization initiator by a standard time, the high-ratefeeding period of the polymerization initiator is defined as a periodfrom 0% to j %, wherein j is 5 to 20, of the standard time, and thestandard time is defined as a passage of time from a beginning of thedropwise addition of the polymerization initiator to a completion of adropwise addition of the second solution (II).
 2. The method of claim 1,wherein: the feeding (II), which is a dropwise addition of the secondsolution, is started after or simultaneously with the start of thedropwise addition of the polymerization initiator to the reactor; α₁:α₂:. . . :α_(n) represents the first composition ratio (in mol %); thefeeding of the first solution (I) is completed before 20% of thestandard time passes; the polymerization initiator is fed in an amountof 30 to 90% by mass of a total feed amount thereof during the high-ratefeeding period and the first composition ratio is determined by: (i)adding dropwise, at a fixed dropping rate, to a reactor containing asolvent: a dropping solution comprising 100 parts by mass of a monomermixture having the same monomer composition ratio as the targetcomposition ratio, α′₁:α′₂: . . . :α′_(n); the polymerization initiator;and the solvent, wherein a composition (in: mol %) M₁:M₂: . . . :M_(n)of the monomers α₁ to α_(n) remaining in the reactor is calculated whena passage of time from the start of the dropwise addition is t₁, t₂, t₃. . . , and t_(m), and a ratio (in: mol %) P₁:P₂: . . . :P_(n) of theconstitutional units α′₁ to α′_(n) of each polymer, formed between thetime t₁ to the time t₂, between the time t₂ to the time t₃, . . . , andbetween the time t_(m) to the time t_(m+1), is calculated; (ii)determining a time zone from t_(m) to t_(m+1) when the ratio P₁:P₂: . .. :P_(n) becomes nearest to the target composition ratio α′₁:α′₂: . . .:α′_(n), wherein m represents an integer of 1 or more; and (iii)determining factors F₁, F₂, . . . , and F_(n) from the value of theratio P₁:P₂: . . . :P_(n) between t_(m) and t_(m+1) and the value of thecomposition ratio M₁:M₂: . . . :M_(n) at the passage of time t_(m) basedon equations F₁=P₁/M₁, F₂=P₂/M₂, . . . , and F_(n)=P_(n)/M_(n), whereinα₁=α′₁/F₁, α₂=α′₂/F₂, . . . ,α_(n)=α′_(n)/F_(n).
 3. The method of claim1, wherein the rate of dropwise addition of the polymerization initiatoris changed during a course of the high-rate feeding period.
 4. Themethod of claim 1, wherein the rate of dropwise addition of thepolymerization initiator is changed after an end of the high-ratefeeding period.
 5. The method of claim 1, wherein the polymerizationinitiator is added continuously.
 6. The method of claim 1, wherein thepolymerization initiator is added intermittently.